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AN    INTRODUCTORY    LOGIC 


AN 


INTRODUCTORY  LOGIC 


BY 


JAMES   EDWIN   CREIGHTON 

SAGE  PROFESSOR  OF  LOGIC  AND  METAPHYSICS  IN  CORNELL 
UNIVERSITY 


NEW  EDITION,   REVISED   AND   CORRECTED 


gorfc. 
THE   MACMILLAN    COMPANY 

LONDON :  MACMILLAN  &  CO.,  LTD. 
I9O2 

All  rights  reserved 


CU>VM 

, 


COPYRIGHT,  1898,  1900 
BY  THE  MACMILLAN  COMPANY. 


Set  up  and  electrotyped  September,  1898.     Reprinted  July, 
1899.     New  Edition,  Revised  and  Corrected,  March,  1900  ; 
April,  October,  1901  ;  July,  1902. 


J.  8.  Gushing  &  Co.  -  Berwick  &  Smith 
Norwood  Mass.  U.S.A. 


GIFT 

/  \ 


C7 

I  zoo 


PREFACE 

THIS  volume  is  intended  primarily  as  a  text-book  for 
college  students,  and  grew  out  of  my  lectures  on  Logic 
to  undergraduate  classes  in  Cornell  University.  It 
aims  at  being  both  practical  and  theoretical.  In  spite  of 
the  obvious  deficiencies  of  formal  Logic  as  a  theory  of 
the  nature  of  thought,  I  am  convinced  that  it  is  one 
of  the  most  valuable  instruments  in  modern  education 
for  promoting  clear  thinking,  and  for  developing  criti- 
cal habits  of  mind.  J.  S.  Mill,  speaking  in  the  Auto- 
biography of  the  discipline  which  he  received  from 
working  logical  exercises,  expresses  the  following 
opinion :  "  I  am  persuaded  that  nothing,  in  modern 
education,  tends  so  much,  when  properly  used,  to  form 
exact  thinkers,  who  attach  a  precise  meaning  to  words 
and  propositions,  and  are  not  imposed  on  by  vague, 
loose,  or  ambiguous  terms."  Although  in  treating  the 
syllogistic  Logic  I  have  followed  to  a  large  extent  the 
ordinary  mode  of  presentation,  I  have  both  here,  and 
when  dealing  with  the  Inductive  Methods,  endeavoured 
to  interpret  the  traditional  doctrines  in  a  philosophical 
way,  and  to  prepare  for  the  theoretical  discussions  of 
the  third  part  of  the  book. 

The  advisability  of  attempting  to  include  a  theory  of 
thought,  or  philosophy  of  knowledge,  even  in  outline, 


M636385 


VI  PREFACE 

in  an  elementary  course  in  Logic,  may  at  first  sight 
appear  doubtful.  It  seems  to  me,  however,  that  this 
inclusion  is  not  only  justifiable,  but  even  necessary  at 
the  present  time.  Psychology  is  no  longer  a  '  philoso- 
phy of  mind ' ;  but,  under  the  influence  of  experimental 
methods,  has  differentiated  itself  almost  entirely  from 
philosophy,  and  become  a  '  natural '  science.  As  a 
natural  science,  it  is  interested  in  the  structure  of  the 
mental  life,  —  the  characteristics  of  the  elementary 
processes,  and  the  laws  of  their  combination,  —  and 
not  primarily  in  the  function  which  ideas  play  in  giving 
us  knowledge.  It  is  clear  that  psychology  does  not 
undertake  to  describe  all  that  mind  is  and  does.  It 
belongs  to  Logic  to  investigate  intelligence  as  a  know- 
ing function,  just  as  it  is  the  task  of  Ethics  to  deal 
with  the  practical  or  active  mental  functions. 

The  practical  question  still  remains  as  to  whether 
this  side  of  Logic  can  be  made  profitable  to  students 
who  have  had  no  previous  philosophical  training.  I 
am  well  aware  of  the  difficulty  of  the  subject,  but  my 
own  experience  leads  me  to  believe  that  the  main  con- 
ceptions of  modern  logical  theory  can  be  rendered 
intelligible  even  to  elementary  classes.  Of  the  incom- 
pleteness and  shortcomings  of  my  treatment  I  am  quite 
conscious ;  but  I  have  endeavoured  to  make  the  matter 
as  simple  and  concrete  as  possible,  and  to  illustrate  it 
by  means  of  familiar  facts  of  experience. 

For  a  number  of  the  practical  questions  and  exer- 
cises, I  am  indebted  to  Professor  Margaret  Washburn 
of  Wells  College;  others  are  original,  or  have  been 
collected  in  the  course  of  my  reading.  I  have  also 


PREFACE  vii 

taken  a  number  of  arguments  from  the  examination 
papers  of  different  universities,  and  from  various  works 
on  Logic,  especially  from  Jevons's  Studies  in  Deductive 
Logic,  from  the  little  volume  entitled  Questions  on  Logic 
by  Holman  and  Irvine  (2d  ed.,  London,  1897),  and  from 
Hibben's  Inductive  Logic. 

In  writing  the  book,  I  have  been  under  obligation  to 
a  large  number  of  writers  and  books.  My  heaviest 
debt  is  doubtless  to  Bosanquet,  and  perhaps  next  in 
order  I  am  under  obligations  to  Mill,  Jevons,  Sigwart, 
and  Bradley.  I  have  also  derived  help  from  Minto's 
Logic,  Deductive  and  Inductive,  the  chapter  on  '  Rea- 
soning '  in  James's  Principles  of  Psychology,  J.  H.  Hys- 
lop's  Elements  of  Logic,  and  from  other  works  to  which 
reference  is  made  throughout  the  book. 

My  colleagues  in  the  Sage  School  of  Philosophy 
have  kindly  aided  me  from  time  to  time  with  advice 
and  encouragement,  and  I  have  also  received  valuable 
suggestions  from  other  teachers  of  Logic  with  whom  I 
have  talked  and  corresponded.  In  particular,  I  wish 
to  express  my  obligations  to  my  former  colleague,  Pro- 
fessor James  Seth,  who  read  nearly  all  of  the  book  in 
manuscript,  and  to  Dr.  Albert  Lefevre,  who  kindly 
assisted  me  in  reading  the  proofs. 

J.  E.  C. 

CORNELL  UNIVERSITY, 
August,  1898. 


TABLE   OF   CONTENTS 

INTRODUCTION 

CHAPTER  I 
THE  STANDPOINT  AND  PROBLEM  OF  LOGIC 

PAGE 

§  I.  Definition  of  the  Subject         . I 

§  2.  Relation  to  Psychology 4 

§  3.  Logic  as  a  Science  and  an  Art 8 

§  4.  The  Material  of  Logic 13 

CHAPTER  II 

IMPORTANT  STAGES  IN  THE  DEVELOPMENT  OF  LOGIC 

§5.  The  Logic  of  the  Greeks  :  Aristotle 18 

§  6.  Logic  during  the  Middle  Ages 26 

§  7.  The  Logic  of  Bacon        . 28 

§  8.  Logic  since  the  Time  of  Bacon 29 

PART  I. -THE  SYLLOGISM 

CHAPTER   III 
THE  SYLLOGISM  AND  ITS  PARTS 

§  9.    The  Nature  of  the  Syllogism 36 

§  10.    The  Parts  of  the  Syllogism 39 

§n.    The  Proposed  Division  of  Mental  Operations          .         „  43 

CHAPTER   IV 
THE  VARIOUS  KINDS  OF  TERMS 

§  12.     Singular,  General,  and  Collective  Terms          ....      46 
§  13.     Abstract  and  Concrete  Terms 48 


TABLE  OF  CONTENTS 


§  14.     Positive  and  Negative  Terms  .         .         .         .         .        .         .  52 

§  15.     Absolute  and  Relative  Terms 54 

§  16.     Extension  and  Intension  of  Terms 55 

CHAPTER   V 
DEFINITION  AND  DIVISION 

§  17.     Fixing  the  Meaning  of  Terms 61 

§  18.     Definition 63 

§  19.     Division 71 

CHAPTER  VI 
PROPOSITIONS 

§  20.    The  Nature  of  a  Proposition 78 

§21.     The  Quality  and  Quantity  of  Propositions       ....  80 

§  22.     Difficulties  in  Classification 83 

§  23.     Formal  Relation  of  Subject  and  Predicate       ....  85 

CHAPTER  VII 
THE  INTERPRETATION  OF  PROPOSITIONS 

§  24.     The  So-called  Process  of  Immediate  Inference        ...  92 

§25.     The  Opposition  of  Propositions 94 

§  26.     The  Obversion  of  Propositions 98 

§  27.     The  Conversion  of  Propositions loo 

CHAPTER  VIII 
THE  SYLLOGISM 

§  28.     The  Nature  of  Syllogistic  Reasoning       .....  105 

§  29.     The  Rules  of  the  Syllogism 108 

§30.     The  Figures  of  the  Syllogism  .         .         .         .         .         .113 

CHAPTER   IX 
THE  VALID  MOODS  AND  THE  REDUCTION  OF  FIGURES 

§31.     The  Moods  of  the  Syllogism .115 

§32.     The  Special  Canons  of  the  Four  Figures          .         .         .         .  117 

§  33.     The  Determination  of  the  Valid  Moods  in  Each  of  the  Figures  120 

§  34.     The  Mnemonic  Lines 122 


TABLE  OF  CONTENTS  XI 

CHAPTER  X 

ABBREVIATED  AND  IRREGULAR  FORMS  OF  ARGUMENT 

PAGE 

§  35.  Enthymemes 126 

§  36.  Episyllogisms  and  Prosyllogisms 127 

§  37.  Sorites,  or  Chains  of  Reasoning 129 

§  38.  Irregular  Arguments 132 

CHAPTER  XI 

HYPOTHETICAL  AND  DISJUNCTIVE  ARGUMENTS 

§  39.    The  Hypothetical  Syllogism 136 

§  40.  Relation  of  Categorical  and  Hypothetical  Arguments      .         .  139 

§  41.     Disjunctive  Arguments 145 

§  42.    The  Dilemma 148 

CHAPTER  XII 

FALLACIES  OF  DEDUCTIVE  REASONING 

§43.  Classification  of  Fallacies 152 

§  44.  Errors  in  Interpretation 154 

§  45.  Formal  Fallacies 157 

§  46.  Material  Fallacies 159 

PART  II. —  INDUCTIVE  METHODS     /^v^^ 

CHAPTER  XIII 
THE  PROBLEM  OF  INDUCTION.  —  OBSERVATION  AND  EXPLANATION 

§47.     The  Problem  of  Induction 172 

§  48.     Observation 176 

§  49.     Explanation 182 

CHAPTER  XIV 

METHODS  OF  OBSERVATION.  —  ENUMERATION  AND  STATISTICS 

§  50.     Enumeration  or  Simple  Counting 185 

§51.     Statistics  and  Statistical  Methods    .         .         .         .      -.         .189 
§52.     The  Calculation  of  Chances 194 


Xll  TABLE  OF  CONTENTS 


CHAPTER  XV 

METHODS  OF  OBSERVATION.  —  DETERMINATION  OF  CAUSAL 
RELATIONS 

PAGE 

§  53.     Mill's  Experimental  Methods  .         .         .         .         .         .         .198 

§  54.     The  Method  of  Agreement      . 200 

§  55.     The  Method  of  Difference       .......     205 

CHAPTER  XVI 

METHODS  OF  OBSERVATION. —  DETERMINATION  OF  CAUSAL 
RELATIONS  (continued} 

§  56.     The  Joint  Method  of  Agreement  and  Difference     .         .         .     209 

§57.     The  Method  of  Concomitant  Variations 21 1 

§  58.    The  Method  of  Residues 213 

CHAPTER    XVII 

METHODS  OF  EXPLANATION.  —  ANALOGY 

§  59.     Explanation  by  Analogy 219 

§  60.     Analogy  as  Suggestive  of  Explanatory  Hypotheses  .         .     223 

§  61.     The  Incompleteness  of  Analogical  Reasoning          .         .         .     226 

CHAPTER   XVIII 
METHODS  OF  EXPLANATION.  —  THE  USE  OF  HYPOTHESES 

§  62.     Reasoning  from  Hypotheses 230 

§  63.  The  Formation  of  Hypotheses         ......  234 

§  64.     The  Proof  of  an  Hypothesis 237 

§  65.     Requirements  of  a  Good  Hypothesis 240 

CHAPTER  XIX 

FALLACIES  OF  INDUCTIVE  REASONING 

§  66.  The  Source  of  Fallacy    .      " 245 

§  67.  Fallacies  due  to  the  Careless  Use  of  Language        .         .         .  246 

§  68.  Errors  of  Observation 250 

§  69.  Mistakes  in  Reasoning 254 

§  70.  Fallacies  due  to  Individual  Prepossessions      ....  257 


TABLE   OF   CONTENTS  xiii 

PART  III.  —  THE  NATURE  OF  THOUGHT 

CHAPTER   XX 
JUDGMENT  AS  THE  ELEMENTARY  PROCESS  OF  THOUGHT 

PAGE 

§  71.  Thinking  the  Process  by  which  Knowledge  grows  or  develops  260 

§  72.  The  Law  of  Evolution  and  its  Application  to  Logic         .         .  262 

§  73.  Judgment  as  the  Starting-point 266 

§  74.  Concepts  and  Judgment .  268 

CHAPTER  XXI 

THE  MAIN  CHARACTERISTICS  OF  JUDGMENT 

§75.    The  Universality  of  Judgments 274 

§  76.     The  Necessity  of  Judgments 276 

§  77.  Judgment  involves  both  Analysis  and  Synthesis       .         .         .  279 

§  78.  Judgment  as  constructing  a  System  of  Knowledge           .         .  284 

CHAPTER  XXII 
THE  LAWS  OF  THOUGHT 

§  79.    The  Law  of  Identity 288 

§  80.     The  Law  of  Contradiction       .......     295 

§  81.     The  Law  of  Excluded  Middle 297 

CHAPTER   XXIII 
TYPES  OF  JUDGMENT 

§  82.    Judgments  of  Quality 300 

§  83.     Judgments  of  Quantity 304 

§  84.     Judgments  of  Causal  Connection 307 

§  85.     Judgments  of  Individuality 315 

CHAPTER  XXIV 
THE  NATURE  OF  INFERENCE.  —  INDUCTION  AND  DEDUCTION 

§  86.     Judgment  and  Inference .318 

§  87.     The  Nature  of  Inference          .         .         .         .         .         .         .     324 

§  88.     Induction  and  Deduction 329 


XIV  TABLE  OF  CONTENTS 

CHAPTER    XXV 

RATIONAL  AND  EMPIRICAL  THEORIES 

PAGE 

§  89.     The  Point  of  View  of  Rationalism 335 

§  90.     The  Doctrine  of  Empiricism 337 

§  91.     Reasoning  from  Particular  to  Particular           ....  340 

§  92.     Reasoning  from  Particulars  to  a  Universal      ....  344 

QUESTIONS  AND  EXERCISES 348 

INDEX 389 


AN    INTRODUCTORY    LOGIC 


INTRODUCTION 

CHAPTER   I 

THE  STANDPOINT  AND  PROBLEM  OF  LOGIC 

§  i.  Definition  of  the  Subject. —  Logic  may  be  defined 
as  the  sconce  of  thought,  or  as  the  science  which  in- 
vestigates the  process  of  thinking.  Every  one  knows, 
in  a  general  way  at  least,  what  is  meant  by  think- 
ing, and  has  noticed  more  or  less  consciously  some 
of  its  peculiarities.  Thinking  is  the  intellectual  act  by 
means  of  which  knowledge  is  obtained.  We  do  not 
really  know  any  fact  until  we  think  it ;  that  is,  until  the 
mind  sets  it  in  its  proper  relation  to  the  other  parts  of 
its  experience,  and  thus  comes  to  understand  its  true 
meaning.  We  make  a  distinction,  for  example,  between 
what  has  come  to  us  through  report  or  hearsay,  and 
conclusions  which  we  have  reached  by  our  own  think- 
ing. 'I  have  heard;  we  say,  'that  A  is  dishonest,  but 
I  do  not  know  it.'  That  is,  this  fact  has  not  been 
reached  as  a  result  of  our  own  thinking,  and  cannot 
therefore  claim  the  title  of  knowledge.  On  the  other 
hand,  that  the  earth  is  round,  is  not  a  mere  matter  of 
hearsay  for  an  educated  man.  It  is  a  piece  of  know- 
ledge, because  it  is  a  conclusion  which  he  has  reached 
by  thinking,  or  by  putting  together  various  facts  for 
himself. 


2  THE   STANDPOINT  AND   PROBLEM  OF  LOGIC 

Logic,  then,  in  dealing  with  thinking,  is  concerned 
with  the  process  by  which  knowledge  is  obtained.  In 
defining  it  as  a  science,  we  mean  that  it  seeks  to  sub- 
stitute exact  and  systematic  knowledge  regarding  the 
nature  of  thought  for  the  popular  notions  to  be  found 
in  everyday  life.  Like  all  the  i^ciences,  logic  has  to 
correct  and  supplement  ordinary*knowledge.  It  is  its 
mission  to  help  us  to  understand  more  exactly  and 
completely  the  way  in  which  thinking  goes  on,  and 
to  discover  the  laws  which  are  followed  in  gaining 
knowledge. 

But  it  is  also  the  business  of  a  science  to  system- 
atize facts.  Logic,  then,  cannot  content  itself  with  a 
mere  description  of  this  or  that  kind  of  thinking,  in 
isolation  from  other  ways  in  which  we  think.  It  must 
also  deal  with  the  way  in  which  the  various  kinds  of 
thinking  are  related.  For  example,  we  apply  such 
terms  as  'conception,'  ' judgment,'  'induction,'  and  'de- 
duction' to  different  intellectual  operations,  and  give 
the  distinguishing  characteristic  in  each  case.  But  it  is 
necessary  as  well  to  understand  how  these  processes 
are  related.  Since  all  thinking  has  one  end,  the  dis- 
covery of  truth,  the  various  intellectual  operations  must 
mutually  cooperate  and  assist  in  this  result.  AlLjof 
the  logical  processes,  then,  stand  in  relation  to  one 
another.  They  are  all  parts  of  the  one  Intelligence, 
though  they  may  well  represent  different  stages  or 
steps  in  its  work  of  obtaining  knowledge.  It  becomes 
the  business  of  logic,  then,  to  show  us  the  organic 
structure  of  thought.  In  other  words,  it  must  furnish 
a  comprehensive  view  of  the  way  in  which  intelligence 

v 


§  i.     DEFINITION   OF  THE  SUBJECT  3 

acts,   and  the  part  which  processes  like  'conception,' 
'judgment,'  'induction,'  etc.,  play. 

(1)  The  word  <•  logic1  is  derived  from  the  adjective  corresponding 
to  the  Greek  noun  Aoyos,  which  signifies  either  a  complete  thought, 
or  a  word  as  the  expression  of  that  thought.     The  singular  form  of 
the  adjective  Aoyi/o/,  from  which  the  English  word  is  derived,  was 
supposed  to  qualify  either  cTncrr^rj  as  applying  to  the  theoretical 
science  of  logic,  or  re\vr]  as  referring  to  the  practical  application 
of  its  rules  and  as  affording  guidance  in  the  art  of  correct  reason- 
ing.    We  shall  have  to  raise  the  question  in  a  subsequent  section 
how  far  it  is  possible  to  regard  logic  as  an  art,  or  a  system  of  rules 
which  teach  us  how  to  reason  correctly. 

(2)  We  have  denned  logic  as  the  science  of  the  operations  and 
processes  of  thought,  or  as  the  science  of  thinking.     It  is  evident, 
however,  that  this  definition  does  not  carry  us  very  far  unless  we 
know  what  thinking  means.     And  to  gain  a  clearer  idea  of  this  com- 
mon term  maybe  said  to  be  the  problem  of  logic.     This  is,  however, 
by  no  means  as  easy  a  task  as  may  at  first  appear.     Familiar  words 
and  phrases  often  conceal  difficulties.    They  are  constantly  repeated 
without  reflection,  and  this  very  frequency  of  repetition  is  likely 
to  prevent  us  from  trying  to  gain  any  clear  ideas  regarding  the 
nature  of  the   objects  which   they  denote.     It   is   only  when  we 
become  discontented  with  our  knowledge   regarding  any  subject, 
when  doubts  arise  whether  we  really  understand  the  meaning  of 
the  words  which  we  use,  that  we  attempt  to  make  our  knowledge 
scientific,  i.e.,  to  gain  clear,  definite,  and  systematic  ideas.     This 
can  perhaps  be  made  clearer  by  considering  the  main  differences 
between  an  educated  and  an  uneducated  man.     The  educated  man 
has,  of  course,  a  great  deal  more  information  than  the  other,  and 
his  knowledge  is  more  definite  and  systematic.     But  a  second  and 
more  important  distinction  is  found  in  the  attitude  of  mind  which 
education  begets.     The  educated  man  is  desirous  of  knowing  more, 
because  he   is   sensible  of  his   own  ignorance.      The  uneducated 
man,  on  the  other  hand,  supposes  that  he  knows  all  about  things 
whose  names  are  familiar  to  him.      He  can  settle  puzzling  theo- 
logical  or  political   problems   off-hand   in    a    way    which   is  per- 


4     THE  STANDPOINT  AND  PROBLEM  OF  LOGIC 

fectly   satisfactory  to   himself,  without  study,  and  almost  without 
reflection. 

It  is  clear  that  no  intellectual  salvation  is  possible  for  a  man  so 
long  as  he  remains  in  this  state  of  mind.  A  sense  of  one's  own 
ignorance  is  the  beginning  of  wisdom.  Socrates,  one  of  the  great 
pioneers  of  science  among  the  Greeks,  and  especially  of  the  sciences 
of  logic  and  ethics,  was  so  firmly  convinced  of  this  that  he  made  it 
the  business  of  his  life  to  go  about  the  streets  of  Athens  and  con- 
vince those  **  who  thought  they  were  wise  and  were  not  wise,"  of 
their  ignorance.  u  And  because  I  did  this,"  he  says  naively,  "  many 
of  them  were  angry,  and  became  my  enemies." 

§  2.  Relation  to  Psychology,  —  It  may  aid  us  in 
obtaining  a  clearer  view  of  what  thinking  is,  if  we 
compare  the  general  standpoint  of  logic  with  that  of 
psychology.  Both  of  these  sciences  deal  with  what 
goes  on  in  mind  or  consciousness,  and  are  thus  opposed 
to  the  so-called  objective  sciences,  which  are  all  con- 
cerned with  some  group  or  field  of  external  facts.  But 
in  spite  of  this  agreement,  there  is  an  important  dis- 
tinction between  logic  and  psychology.  In  the  first 
nlace,  psychology  deals  with  all  that  there  jsjn_jnmd. 
xWt  describes  pleasures  and  pains,  acts  of  will,  and  the 
association  of  ideas,  as  well  as  what  is  usually  called 
logical  thinking.  But  logic  does  not  differ  from  psy- 
chology simply  by  being  less  inclusive  than  the  latter. 
It  is  true  that,  from  the  standpoint  of  psychology,  the 
thought-process  is  merely  a  part  of  the  mental  content, 
which  has  to  be  analyzed  and  described  like  anything 
else  which  goes  on  in  consciousness.  Thinking  has 
doubtless  for  psychology  peculiar  marks  or  charac- 
teristics which  distinguish  it  from  other  related  pro- 
cesses like  those  of  association;  but  when  these  have 


§  2.    RELATION  TO  PSYCHOLOGY  5 

been  found,  and  the  psychological  description  of  think- 
ing is  complete,  the  question  with  which  logic  deals  has 
not  yet  been  raised.  For  logic,  as  we  shall  see  pres- 
ently, adopts  a  different  standpoint,  and  investigates 
with  a  different  end  in  view. 

The  important  difference  is  this :  In  psychology  we 
are  interested  in  the  content  of  consciousness  for  its 
own  sa£e,_pu\d  just  as  it  stands.  We  try  to  find  out 
what  actually  goes  on  in  our  minds,  and  to  describe  it 
just  as  we  should  any  event  which  occurs  in  the  exter- 
nal world.  But  in  logic  the  question  is  not :  What  are 
mental  processes?  but  rather:  What_knowledge  do 
they  give  us,  and Js_this  knowledge  true  or  false? 
Logic,  in  other  words,  does  not  regard  the  way  in 
which  ideas  exist,  and  is  not  interested  in  them  for 
what  they  are,  but  rather  in  the  purpose  which  they  sub- 
serve in  affording  us  knowledge  of  something  beyond 
themselves.  Psychology,  in  its  description  of  conscious 
states,  inquires  regarding  their  quality,  intensity,  dura- 
tion, etc.,  and  the  ways  in  which  they  combine  with 
each  other  to  form  complex  ideas.  The  problem  with 
which  logic  is  concerned,  on  the  other  hand,  has  refer- 
ence to  the  value  of  ideas  when  they  are  taken  to 
represent  facts  in  the  real  world.  In  other  words,  the 
question  which  logic  raises  is  not  regarding  the  actual 
character  of  ideas  as  existing  processes,  but  regarding 
their  value  or  significance  as  pieces  of  knowledge. 

(i)  The  relation  between  logic  and  psychology  may  perhaps  be 
illustrated  by  referring  to  that  which  exists  between  morphology 
and  physiology.  Morphology  deals  with  the  form  and  structure 
of  living  organisms,  and  physiology  with  the  various  acts  and  func- 


6  THE   STANDPOINT  AND   PROBLEM   OF  LOGIC 

tions  which  these  organisms  discharge.  Thus  we  speak  of  the 
former  as  the  science  of  form  or  structure,  and  of  the  latter  as  the 
science  of  function.  In  the  same  way,  psychology  may  be  said  to 
deal  with  the  actual  structure  of  mental  processes,  and  logic  with 
the  part  which  they  play  in  giving  us  knowledge. 

It  must  be  noticed,  however,  that  this  is  a  distinction  made  for 
purposes  of  investigation,  and  does  not  denote  that  structure  and 
function  have  nothing  to  do  with  each  other.  On  the  contrary, 
some  knowledge  of  the  function  is  often  necessary  in  order  to  under- 
stand the  structure  of  an  organ  ;  and,  on  the  other  hand,  it  is  usually 
true  that  the  nature  of  a  function  only  becomes  completely  intelligi- 
ble when  the  character  of  the  mechanism  with  which  it  works  is 
known.  And  the  same  holds  true,  I  think,  of  the  relations  between 
psychology  and  logic.  Although  it  has  been  found  profitable  when 
dealing  with  consciousness,  as  in  the  biological  realm,  to  investigate 
the  nature  of  structure  and  function  separately,  yet  here,  as  there, 
the  two  lines  of  inquiry  cross  each  other ;  for  it  is  beyond  question 
that  the  knowledge  we  obtain  by  thinking  is  largely  dependent  upon 
the  character  (quality,  intensity,  etc.)  of  the  actual  processes  in  con- 
sciousness. To  understand  the  nature  of  a  logical  idea,  then,  it  is 
often  necessary  to  refer  to  the  psychological  facts  and  their  actual 
mode  of  behaviour.  And  it  is  equally  true  that  one  cannot  carry 
on  a  psychological  investigation  into  the  nature  of  mental  processes 
without  taking  account,  to  some  extent,  of  the  part  which  they  play 
in  giving  us  knowledge.  No  psychology  is  able  to  take  ideas  simply 
as  existing  conscious  processes  to  which  no  further  meaning  or 
importance  attaches ;  it  is  only  with  reference  to  the  function  they 
perform  as  knowing  states  that  their  own  peculiar  character  can  be 
understood.  In  other  words,  the  intellectual  activities  and  purposes 
of  mind  must  be  presupposed  in  psychology,  though  this  science,  for 
the  most  part,  goes  its  way  as  if  the  ideas  were  not  cognitive  at  all. 
At  least  this  seems  to  be  true  of  the  'new'  or  experimental  psy- 
chology as  opposed  to  the  philosophies  of  mind. 

(2)  It  would  of  course  be  presumptuous,  as  well  as  utterly  useless, 
for  any  writer  to  draw  a  hard  and  fast  line  between  logic  and  psy- 
chology, and  to  forbid  others  to  overstep  it.  In  attempting  to  dis- 


§  2.     RELATION  TO.  PSYCHOLOGY  7 

cover  the  dividing  line  between  two  closely  related  sciences  one 
must  be  guided  by  the  procedure  of  those  who  are  working  in  the 
fields  which  it  is  proposed  to  divide.  Now,  it  must  be  admitted  that 
by  no  means  all  of  the  recent  writers  in  psychology  limit  the  sphere 
of  their  science  in  the  way  above  described ;  that  is,  there  are 
certain  psychologists  who  do  not  confine  their  attention  to  the  mere 
mental  processes  as  such,  but  include  in  their  investigations  the  fur- 
ther problem  regarding  the  part  which  these  processes  play  in  giving 
us  knowledge.  Thus  in  Professor  James's  Principles  of  Psychology 
there  is  an  excellent  chapter  on  t  Reasoning'  which  certainly  con- 
tains as  much  logical  as  psychological  matter.  In  the  same  way, 
one  finds  problems  of  knowledge  discussed  in  the  psychological 
writings  of  Professor  Ladd,  and  also,  to  some  extent,  in  the  recent 
work  by  Mr.  Stout  entitled  Analytic  Psychology.  In  spite  of  this, 
it  is  evident  that  the  tendency  of  the  *  new,'  or  laboratory  psy- 
chology, is  towards  a  sharper  differentiation  of  its  problems  from 
those  of  logic.  The  '  natural  science  of  psychology '  is  interested 
in  the  conscious  process  as  an  event  in  time  with  certain  defi- 
nitely ascertainable  characteristics.  It  is  perhaps  not  a  matter  of 
great  moment  whether  the  name  'psychology'  be  limited  to  this 
kind  of  inquiry,  or  whether  philosophical  inquiries  regarding  the 
nature  of  knowledge  be  also  included  under  it.  I  have  assumed, 
however,  in  this  section,  that  psychology  is  now  being  differentiated 
from  the  more  general  inquiries  regarding  the  nature  of  mind,  and 
that  it  has  taken  for  its  field  of  investigation  the  nature  of  mental 
processes  regarded  merely  as  mental  processes. 

Consider  a  little  further  the  nature  of  the  ideas  with 
which  logic  deals.  Every  idea,  as  we  have  seen,  not 
only  exists  in  some  definite  fashion  in  some  particular* 
consciousness,  connected  with  certain  other  ideas,  and 
with  a  definite  quality,  intensity,  etc.,  but  it  has  a  mean- 
ing or  significance  as  a  piece  of  knowledge.  It  not 
only  is  something,  but  it  also  stands  for  or  signifies 
something.  Now  it  is  not  with  the  existence,  but  with 


8  THE   STANDPOINT  AND   PROBLEM   OF   LOGIC 

the  meaning  side  of  ideas  that  logic  has  to  do.  A 
logical  idea,  or  piece  of  knowledge,  is  not  merely  a 
modification  of  consciousness  which  exists  in  the  mind 
of  some  individual  at  a  particular  time.  For  example, 
the  proposition  :  *  The  three  angles  of  a  triangle  are 
equal  to  two  right  angles,'  will  give  rise  to  a  number 
of  definite  psychological  processes  (probably  auditory 
or  visual  in  character)  in  the  mind  of  any  individual. 
These  processes  would  also  probably  differ  in  character 
in  the  case  of  two  persons.  The  meaning  of  the  propo- 
sition, however,  is  distinct  from  the  definite  processes 
which  arise  in  particular  minds.  The  proposition  has 
a  significance  as  an  objective  fact,  or  piece  of  know- 
ledge, outside  my  mind ;  the  psychological  images  or 
processes  may  differ  for  different  persons,  but  the  fact 
expressed  is  the  same  for  all  minds  and  at  all  times. 

§  3.  Logic  as  a  Science  and  an  Art. — We  have  de- 
fined logic  as  the  science  of  thought,  but  it  has  often 
been  pointed  out  that  there  are  equally  strong  reasons 
for  considering  it  to  be  an  art.  Jevons  makes  the 
distinction  between  a  science  and  an  art  very  clear  by. 
saying  that  "a^  science  teaches  us  to  know,  and  an  art 
to  do."  A  science  is  interested  in  the  discovery  of  facts 
and  laws  without  any  thought  of  what  use  may  be  made 
of  this  knowledge;  an  art,  on  the  contrary,  gives  practi- 
cal guidance  and  direction  for  some  course  of  action. 
The  question  before  us,  then,  is  this :  Does  logic  merely 
give  us  knowledge  about  the  ways  in  which  we  think, 
or  does  it  also  help  us  to  think  rightly  ? 

Before  we  attempt  to  answer  this  question,  we  must 


§  3.     LOGIC  AS  A   SCIENCE  AND  AN  ART  9 

note  that  practical  rules  of  action  are  based  upon  sci- 
entific knowledge.  An  art,  in  other  words,  depends 
upon  science,  and  grows  in  perfection  with  the  advance 
of  scientific  knowledge.  Thus  medicine,  as  the  art  of 
healing,  is  founded  upon  the  sciences  of  chemistry, 
physiology,  and  anatomy,  and  it  is  because  of  the  great 
discoveries  which  have  been  made  in  these  fields  within 
recent  years,  that  it  has  been  able  to  advance  with  such 
gigantic  strides.  Again,  the  art  of  singing,  in  so  far  as 
it  is  an  art  which  can  be  taught  and  learned,  depends 
upon  a  knowledge  of  the  physical  and  physiological 
laws  of  the  vocal  organs.  An  art,  then,  always  pre- 
supposes a  certain  amount  of  science,  or  knowledge, 
and  is  simply  the  application  of  this  knowledge  to  some 
practical  purpose.  In  some  cases  the  application  is 
very  obvious  and  direct ;  in  others,  it  is  much  more 
difficult  to  determine ;  but,  in  general,  there  is  always 
this  relation  between  theory  and  practice,  between 
knowing  and  doing. 

From  what  has  been  already  said,  it  will  be  evident 
that  logic  must  first  be  a  science  before  it  can  become 
an  art.  Its  first  business  must  be  to  investigate  the 
nature  of  thought,  and  to  attempt  to  discover  the  differ- 
ent forms  which  the  latter  assumes  in  the  course  of  its 
development.  So  that  we  were  right  in  defining  it  as 
primarily  a  science.  But  the  further  question  remains : 
How  far  is  it  possible  to  apply  the  laws  of  logic  after 
they  have  been  discovered  in  such  a  way  as  to  obtain 
directions  how  to  reason  correctly  in  every  case  ?  Can 
we  not  apply  our  knowledge  of  the  laws  of  thought  in 
such  a  way  as  to  get  a  complete  art  of  reasoning,  just  as 


IO          THE  STANDPOINT  AND   PROBLEM   OF  LOGIC 

the  laws  of  chemistry  and  biology  are  applied  in  medi- 
cine ? 

It  is  no  doubt  true  in  logic,  as  everywhere,  that  scien- 
tific knowledge  is  capable  of  practical  application.  But 
I  do  not  think  that  logic  can  be  regarded  as  an  art,  in 
the  sense  that  it  furnishes  a  definite  set  of  rules  for 
thinking  correctly.  There  is  an  important  distinction 
in  this  case  which  must  not  be  left  out  of  account.  The 
physical,  and  even  the  biological  sciences,  deal  with 
things  whose  way  of  acting  is  perfectly  definite  and 
uniform.  The  character  of  any  of  the  physiological 
functions,  as,  e.g.,  digestion,  may  be  comparatively  com- 
plex and  difficult  to  determine,  but  it  always  attains  its 
end  through  the  use  of  the  same  means.  When  once  its 
laws  are  understood,  it  is  not  difficult  to  prescribe  just 
how  the  proper  means  may  always  be  secured  for  the 
attainment  of  the  desired  end.  But  thinking  has  much 
more  flexibility  in  its  way  of  acting.  We  cannot  say 
with  the  same  definiteness  as  in  the  cases  we  have  been 
considering,  that  in  order  to  reach  a  certain  end  we  must 
use  a  definite  set  of  means.  It  is  not  possible,  that  is, 
to  say :  If  you  would  learn  what  is  true  about  this  sub- 
ject, you  must  follow  this  rule  and  that  in  your  thinking. 
Logic,  it  seems  to  me,  cannot  be  regarded  as  an  art  like 
photography,  or  even  like  medicine ;  for  it  is  not  possible 
to  lay  down  definite  rules  for  the  guidance  of  thinking 
in  every  case.  What  we  can  do,  is  to  show  the  method 
by  which  new  truths  have  been  discovered,  and  the 
general  conditions  which  must  always  be  fulfilled  in 
reasoning  correctly.  And  it  is  also  possible  to  point 
out  the  more  common  errors  which  arise  when  these 


§  3.    LOGIC  AS  A  SCIENCE  AND  AN  ART  1 1 

conditions  are  violated.  But  it  is  beyond  the  power  of 
logic  to  formulate  any  definite  set  of  rules  for  the 
guidance  of  thinking  in  every  case. 

We  have  found  that  we  must  give  up  all  extravagant  hopes 
of  the  practical  advantages  to  be  gained  from  a  study  of  logic. 
There  is  no  set  of  rules  which  will  make  us  infallible  reasoners. 
That  being  admitted,  the  question  may  be  raised  as  to  the  utility  of 
the  study.  What  will  it  profit  us  to  devote  ourselves  to  this  subject? 
It  might  be  a  sufficient  answer  to  point  out  that  this  question  pre- 
supposes that  knowledge  has  always  some  ulterior  motive.  The 
assumption  upon  which  it  is  based  is,  in  other  words,  that  the  prac- 
tical advantages  arising  from  any  study  furnish  the  only  justification 
for  undertaking  it.  But  it  is  scarcely  necessary  to  say  that  this  is  not 
an  attitude  which  any  student  should  adopt.  A  student  is  one  who 
prosecutes  a  study  for  its  own  sake,  with  no  other  motive  than  the 
desire  to  know.  And  to  such  a  person  logic  should  not  be  without 
interest.  For  as  we  have  seen,  it  is  an  inquiry  into  the  nature  of 
intelligence.  Its  results,  therefore,  are  not  in  themselves  less  in- 
teresting or  less  important  than  a  knowledge  of  the  various  forms 
of  geological  formation,  or  of  plant  or  animal  life.  "If  it  is  re- 
garded as  a  valuable  achievement,"  says  Hegel,  "  to  have  discovered 
sixty  odd  species  of  parrot,  a  hundred  and  thirty-seven  species  of 
veronica,  and  so  forth,  it  should  surely  be  held  a  far  more  valuable 
achievement  to  discover  the  forms  of  reason."1 


The  necessity  of  devoting  oneself  to'a  science  quite 
unselfishly  cannot  be  too  strongly  enjoined,  nor  the  evils 
which  arise  when  one  begins  a  study  greedy  '  for  quick 
returns  of  profit,'  too  often  emphasized.  Nevertheless, 
since  the  question  has  been  raised,  it  would  not  be  just 
to  refuse  altogether  to  speak  of  the  particular  results 

1  Hegel,  Werke,  Ed.  V.,  p.  139.  Quoted  by  Bosanquet  at  the  beginning 
of  his  work  on  Logic. 


12  THE  STANDPOINT  AND   PROBLEM   OF  LOGIC 

arising  from  a  study  of  logic.  As  we  have  seen,  we 
cannot  hope  to  become  infallible  reasoners  by  its  aid. 
It  is  just  as  true  here  as  in  any  other  field,  however, 
that  knowledge  is  power,  and  ignorance  synonymous 
with  weakness:  For  even  if  one  resolves  never  to  look 
inside  a  logic  book,  one  must  nevertheless  have  some 
theory,  or  act  upon  some  principle  —  it  may  be  quite 
unconsciously  —  in  deciding  what  is  true  and  what  is 
false.  For  instance,  a  man  may  act  upon  the  principles 
that  those  things  are  likely  to  be  true  which  are  favour- 
able to  his  own  interests,  or  which  agree  with  his  own 
prejudices,  or  with  the  articles  of  his  church  or  political 
party.  Or  again,  he  may  regard  his  senses  as  the 
standards  of  truth.  Mr.  Bradley  says  that  if  dogs 
reason,  they  proceed  upon  the  principle,  *  what  smells, 
exists,  and  what  does  not  smell  does  not  exist.'  It  is  not 
uncommon  to  hear  it  announced  :  What  can  be  perceived 
through  the  senses  is  true ;  what  cannot  be  sensed,  or  is 
contrary  to  the  testimony  of  the  senses,  is  an  absurdity. 
This  was  the  standard  of  truth  adopted,  for  example;  by 
those  who  attempted  to  overthrow  the  Copernican  theory 
by  declaring  it  to  be  in  plain  contradiction  to  the  tes- 
timony of  the  senses. 

It  seems  evident,  therefore,  that  intellectual  beings 
cannot  escape  some  kind  of  logical  theory,  whether  they 
hold  it  consciously  or  unconsciously.  It  is  clear,  too, 
that  the  character  of  this  theory  will  determine  to  a 
great  extent  their  thoughts  and  opinions.  The  only 
question  which  remains  is  whether  it  is  better  to 
leave  this  matter  entirely  to  chance,  or  to  attempt  to 
gain  some  clear  ideas  regarding  the  nature  of  thinking, 


§4-    THE   MATERIAL  OF   LOGIC  13 

and  the  conditions  under  which  knowledge  arises.  It 
can  scarcely  be  doubted  that,  even  from  a  practical  point 
of  view,  a  true  theory  is  better  than  a  false  one.  A 
man  who  has  reflected  upon  the  nature  of  proof,  and  the 
principles  of  reasoning,  is  much  less  likely  to  be  deceived 
than  one  who  is  guided  unconsciously  by  assumptions 
which  he  has  never  examined.  It  is  always  an  advan- 
tage to  know  exactly  the  nature  of  the  result  at  which 
we  are  aiming,  and  to  be  perfectly  clear  as  to  our  own 
purposes.  And  this  is  just  what  a  study  of  logic  aids 
us  in  attaining.  It  helps  us  to  understand  the  structure 
of  knowledge  and  conditions  of  proof.  Moreover,  it 
engenders  the  habit  of  criticising  propositions,  and  ex- 
amining the  evidence  upon  which  they  rest.  Further, 
the  importance  of  this  study  for  a  theory  of  education 
may  well  be  emphasized.  For  education,  at  least  so 
far  as  it  undertakes  to  train  the  knowing  powers  of 
the  individual,  must  be  based  upon  a  knowledge  of  the 
necessary  laws  of  intelligence,  and  of  the  steps  or  stages 
which  it  passes  through  in  its  process  of  development. 


§  4.  The  Material  of  Logic.  —  The  business  of  logic, 
as  we  have  seen,  is  to  discover  the  laws  of  thought  and 
to  show  the  differences  which  exist  between  real  and 
imaginary  knowledge.  Where  now  shall  we  find  the 
materials  for  this  study  ?  Where  are  the  facts  which 
are  to  be  taken  as  a  starting-point  ?  It  is,  of  course, 
impossible  to  learn  directly  from  one's  own  conscious- 
ness all  that  thinking  is,  or  everything  of  which  it  is 
capable.  For,  quite  apart  from  the  difficulty  of  observ- 
ing the  process  of  thought  while  it  is  actually  going  on, 


•--  v 


/*    A 


14  THE   STANDPOINT  AND    PROBLEM   OF  LOGIC 

no  one  can  suppose  that  his  own  mind  furnishes  an 
example  of  all  that  thinking  has  done,  or  can  do.  It  is 
necessary  to  take  a  broader  view,  and  learn  how  other 
men  think.  Of  course,  we  cannot  look  into  the  con- 
sciousness of  other  men,  but  we  can  study  the  products 
and  results  of  their  thoughts.  The  history  of  the  way 
in  which  truth  has  been  discovered  is  of  the  greatest 
importance  for  logic.  It  must  not  be  forgotten  that 
thought  is  not  a  thing  which  can  be  described  once  for 
all.  It  is  rather  a  living  activity,  which  is  constantly 
showing  what  it  is  in  what  it  does.  The  history  of  the 
various  sciences  furnishes  a  record  of  the  steps  by  means 
of  which  thought  has  built  up  knowledge.  And,  in  this 
record,  we  have  also  a  revelation  of  the  nature  of  the 
thinking  process  itself,  and  of  the  stages  through  which 
it  has  passed  in  the  course  of  its  development. 

(it  is  by  a  reflection,  then,  upon  the  nature  of  proposi- 
tions which  are  universally  regarded  as  true  that  the 
laws  of  logic  are  obtained)  There  is  always  a  permanent 
body  of  knowledge  which  no  one  thinks  of  calling  in 
question.  Both  in  everyday  knowledge,  and  in  the 
sciences,  there  is  always  found  a  great  number  of  propo- 
sitions which  appear  true  to  everybody.  And  it  is  here 
that  logic  finds  its  material.  Taking  the  facts  and  propo- 
sitions which  are  recognized  as  certain  by  everybody, 
logic  examines  their  structure  in  order  to  learn  about 
the  nature  of  the  intellectual  processes  by  which  they 
have  been  discovered.  What  principles,  it  asks,  are 
involved  in  those  pieces  of  knowledge,  and  what  partic- 
ular acts  of  thougiit  were  necessary  to  discover  them  ? 
It  is  only  by  examining  various  pieces  of  knowledge. 


§4.     THE  MATERIAL  OF  LOGIC  15 

in  this  way,  and  attempting  to  trace  out  the  conditions 
of  their  discovery,  that  one  can  learn  anything  new 
regarding  the  laws  and  character  of  thought.  In  other 
words,  there  is  no  way  of  learning  about  thinking  ex- 
cept by  studying  what  it  has  done.  The  best  way  of 
getting  information  about  what  thought  can  do,  is  to 
study  what  it  has  already  accomplished. 

Every  piece  of  knowledge,  as  the  product  of  thinking,  is  to  some 
extent  a  revelation  of  the  nature  of  intelligence.  But  scientific 
knowledge  —  by  this  I  mean  the  results  of  the  philosophical  and 
historical  sciences  as  well  as  of  the  so-called  natural  sciences  — 
exhibits  perhaps  most  clearly  the  nature  of  thought.  For  the 
history  of  these  sciences  enables  us  to  see  the  process  of  know- 
ledge, as  it  were,  in  the  making.  In  tracing  the  history  of  philo- 
sophical and  scientific  ideas,  we  are  at  the  same  time  following 
the  laws  of  the  development  of  thought.  It  is  this  fact  which 
makes  the  history  of  philosophy  and  of  the  various  sciences  so 
•instructive.  It  was  with  this  object  in  view,  to  take  but  a  single 
example,  that  Whewell  wrote  his  famous  History  of  the  Inductive 
Sciences.  He  was  interested,  that  is,  not  so  much  in  the  mere  facts 
and  names  with  which  he  dealt,  as  in  showing  the  nature  of  thinking 
and  the  methods  which  had  been  employed  in  gaining  a  knowledge 
of  the  world.  This  is  made  very  clear  in  the  introduction  to  another 
work  of  Whewell  from  which  I  quote:  "We  may  best  hope  to 
understand  the  nature  and  conditions  of  real  knowledge  by  studying 
the  nature  and  conditions  of  the  most  certain  knowledge  which  we 
possess  ;  and  we  are  most  likely  to  learn  the  best  methods  of  discov- 
ering truth  by  examining  how  truths,  now  universally  recognized, 
have  really  been  discovered.  Now  there  do  exist  among  us  doc- 
trines of  solid  and  acknowledged  merit  certainly,  and  truths  of  which 
the  discovery  has  been  received  with  universal  applause.  These 
constitute  what  we  commonly  term  sciences ;  and  of  these  bodies  of 
exact  and  enduring  knowledge  we  have  within  our  reach  so  large  a 
collection  that  we  may  hope  to  examine  them  and  the  history  of 


1 6          THE  STANDPOINT  AND   PROBLEM   OF  LOGIC 

their  formation  with  a  good  prospect  of  deriving  from  the  study  such 
instruction  as  we  need  seek.1'1 

We  have  been  insisting  that  the  materials  for  the 
study  of  logic  are  to  be  found  mainly  in  the  records 
which  we  possess  of  what  thinking  has  actually  accom- 
plished. Our  own  consciousness,  it  was  said,  can  supply 
but  a  very  small  quantity  of  material.  To  learn  what 
thinking  is,  one  must  have  as  broad  a  survey  as  possible 
of  its  achievements. 

But  there  is  another  side  to  the  matter.  It  must  never 
be  forgotten  that  it  is"  the  actual  operations  of  thought 
with  which  logic  is  concerned.  The  words  and  proposi- 
tions which  express  the  results  of  thinking  must  never  be 
allowed  to  take  the  place  of  the  thoughts  themselves. 
Now,  we  cannot  directly  study  the  thoughts  of  any  other 
individual.  It  is  only  in  so  far  as  we  interpret,  through 
our  own  consciousness,  the  records  of  what  thinking  has 
done,  that  these  records  are  able  to  throw  any  light 
upon  the  problem  of  logic.  So  in  this  study,  as  else- 
where, we  must  find  the  key  to  the  material  in  our  own 
consciousness.  If  we  are  to  gain  any  real  ideas  of  the 
character  of  the  thinking  processes  by  means  of  which 
the  sciences  have  been  built  up,  we  must  reproduce 
these  in  our  own  minds.  One's  own  consciousness 
must  after  all  furnish  the  key  which  makes  intel- 
ligible the  account  of  the  various  steps  which  the 
thought  of  mankind  has  taken  in  building  up  science 
or  knowledge. 

1  Whewell,  History  of  Scientific  Ideas,  3d  ed.,  Vol.  I.,  p.  4. 
SftjMLWv^*OLMJ\      **»  C*~  i         ^ 

•i«  ^          ,1  A- 


,  v  •• 
-  ,\&\- 


§  4-    THE  MATERIAL  OF   LOGIC  1 7 

References 

The   following    references    may   be   given   in  connection  with 
§§  i  and  2  :  — 

C.  Sigwart,  Logic,  Vol.  I.,  General  Introduction. 
F.  H.  Bradley,  The  Principles  of  Logic,  pp.  i-io. 
B.  Bosanquet,  Logic,  Vol.  I.,  Introduction. 

H.  L.  Mansel,  Prolegomena  Logica,  Chap.  I. 
R.  Adamson,  The  first  part  of  the  article  '  Logic '  in  the  Encyclo- 
pcedia  Britannic  a. 

D.  G.   Ritchie,  The  Relation  of  Logic  to  Psychology,  Philos. 
Review,  Vol.  V.,  pp.  585-600,  Vol.  VI.,  pp.  1-17. 

fK  V>^M  C  •A^Or-rK^x 


CHAPTER  II 

IMPORTANT  STAGES  IN  THE  DEVELOPMENT  OF  LOGIC 

§  5.    The   Logic   of  the   Greeks :    Aristotle.  —  In   the 

fourth  and  fifth  centuries  before  Christ,  a  great  interest 
in  debate  and  public  controversy  sprang  up  in  Athens. 
There  were  several  reasons  for  this.  In  the  first  place, 
the  Athenians  of  this  period  were  a  very  acute  and  intel- 
lectual people ;  they  therefore  required  some  outlet  for 
their  mental  activities.  The  various  sciences  of  nature 
which  occupy  so  much  of  the  thought  of  the  modern 
world  did  not  exist  at  that  time,  nor  did  the  interest  exist 
which  was  necessary  to  create  them.  For  although  the 
Greeks  of  this  period  had  the  greatest  love  and  rever- 
ence for  nature,  their  interest  in  natural  objects  was 
rather  like  that  of  the  poet  and  the  artist,  than  that  of 
the  modern  man  of  science ;  in  other  words,  they  were 
content  to  enjoy  the  beauty  of  natural  objects,  and  to 
take  delight  in  the  harmonies  of  sound  and  color  which 
their  senses  presented  to  them.  They  had  no  desire  to 
pull  things  to  pieces  to  see  how  they  are  made,  or  to 

C  discover  the  laws  according  to  which  they  act,  and  so 
their  mental  energy  and  mental  acuteness  found  its 
chief  outlet  in  argumentative  controversy,  and  public 
debating  became  one  of  their  favourite  diversions.  The 
Athenians  of  those  days  used  to  argue,  from  the  pure 
love  of  argument,  wherever  they  met,  —  in  the  market- 

18 


§  5.    THE  LOGIC  OF  THE  GREEKS  19 

place,  in  the  groves  and  gardens,  and  at  their  meals  and 
banquets. 

There  was  in  addition,  however,  a  very  practical 
reason  why  it  was  necessary  and  desirable  for  one  to 
be  able  to  argue  well.  A  man  of  property  in  Athens 
was  constantly  exposed  to  lawsuits,  and  was  obliged  to 
be  his  own  lawyer  and  defend  his  cause  by  pleading 
before  the  judges.  It  was  of  the  utmost  practical 
importance,  then,  that  he  should  be  able  to  state  his 
cause  well,  and  should  be  master  of  all  the  arts  by 
which  the  judges  would  be  likely  to  be  influenced. 
Under  these  circumstances,  it  is  not  difficult  to  under- 
stand why  the  art  of  public  speaking  came  to  be 
regarded  in  Athens  as  a  necessary  part  of  education. 
And,  in  response  to  this  demand,  there  arose  a  class  of 
teachers  called  Sophists,  who  made  it  their  business  to 
instruct  young  men  in  all  the  practical  affairs  of  life, 
and  especially  in  the  art  of  public  speaking,  or  rhetoric, 
as  it  was  called.  The  Sophists  do  not  seem  to  have 
made  it  their  object  to  teach  truth  to  their  pupils,  or 
to  inculcate  in  them  a  love  and  reverence  for  truth; 
they  rather  sought  to  make  those  whom  they  taught 
clever  men  of  the  world.  In  teaching  the  art  of  argu- 
mentation or  public  speaking  they  did  not  seek  to  point 
out  the  methods  by  which  true  conclusions  could  be 
reached,  but  rather  taught  the  arts  by  which  the  judges 
could  be  persuaded,  and  tricks  for  the  discomfiture  of 
one's  adversary.  The  rhetoric  of  the  Sophists,  in  other 
words,  was  not  a  science  of  reasoning,  but  an  art  of 
persuasion  and  of  controversy.  It  was  not  necessary 
to  have  any  real  knowledge  of  the  subject  under  dis- 


Wir 


20  DEVELOPMENT  OF  LOGIC 

cussion  in  order  to  argue  well,  but  only  to  be  well 
versed  in  all  the  arts  of  persuasion,  and  quick  to  take 
advantage  of  the  omissions  of  an  opponent. 

The  theory  on  which  the  teaching  of  the  Sophists 
was  based  is  usually  known  as  scepticism.  /  The 
Sophists,  that  is,  had  come  to  the  conclusion  that  it 
is  impossible  to  find  any  fixed  standard  of  truth. 
Looking  at  the  diversity  of  individual  opinions  and 
of  individual  feelings,  they  declared  that  knowledge 
or  truth  as  something  objective,  or  the  same  for  all, 
is  an  illusion.  Only  individual  opinions  exist;  there  is 
no  standard  by  reference  to  which  these  opinions  may 
be  measured.  It  is  impossible,  then,  to  distinguish 
false  opinions  from  true.  Indeed,  the  words  '  truth ' 
and  '  falsehood '  can  have  no  real  meaning ;  each  indi- 
vidual must  be  the  measure  of  truth  for  himself. 

Moreover,  in  the  opinion  of  the  Sophists,  the  same 
state  of  things  exists  with  regard  to  our  moral  ideas. 
There  is  no  standard  of  right  and  wrong,  just  as  there 
is  no  standard  of  truth  and  falsehood.  Each  man 
has  the  right  to  choose  what  he  regards  as  most 
advantageous  for  himself.  The  traditional  rules  of 
morality  have  no  authority  over  the  individual,  nor  is 
it  possible  to  discover  any  rules  of  morality  which  are 
binding  on  all  men.  It  is  the  part  of  wisdom  to  con- 
sult one's  own  interest  in  acting,  and  to  seek  to  secure 
one's  own  advantage.  Moral  distinctions,  like  logical 
distinctions,  are  purely  relative  and  individual. 

Socrates  was  the  great  opponent  of  the  ethical  scepti- 
cism of  the  Sophists.  They  had  concluded,  from  the 
diversity  of  individual  opinion  on  moral  questions,  that  - 

-\\  vV: 


§5-  THE  LOGIC  OF  THE  GREEKS         21 

there  is  no  real  or  absolute  distinction  between  right  and 
wrong.  Socrates,  however,  was  convinced  that,  if  one  ex- 
amined more  carefully  the  nature  of  the  judgments  which 
men  pass  on  matters  of  right  and  wrong,  one  would  find 
common  elements  or  ideas.  It  is  possible,  he  believed, 
to  find  a  fixed  standard,  both  in  matters  of  theory  and  in 
matters  of  practice.  This  common  element,  however, 
is  not  to  be  discovered  in  sensation,  nor  in  feelings  of 
pleasure  and  pain ;  these  are  purely  individual,  and 
can  never  serve  as  a  universal  standard.  But  beneath 
the  diversity  of  sensation  and  feelings  there  is  the 
thought,  or  concept,  which  is  common  to  all  men. 
When  rational  beings  come  to  understand  each  other, 
they  must  agree  as  to  the  nature  of  the  fundamental 
virtues, — justice,  temperance,  courage,  etc.  It  is  true 
that  few  men  have  thought  about  these  matters,  arid 
are  able  to  express  their  meaning  clearly;  but  every 
man,  as  a  rational  being,  carries  these  fundamental 
notions  in  his  mind.  Now,  in  order  to  refute  the 
moral  scepticism  of  the  Sophists  (and  it  was  this  side 
of  their  teaching  which  Socrates  especially  opposed), 
it  is  necessary  that  the  ethical  notions,  or  concepts, 
which  are  implicit  in  the  minds  of  men  shall  be  drawn 
out  and  carefully  defined.  How  is  this  to  be  accom- 
plished? Socrates  did  not  undertake  to  teach  men 
what  ideas  they  should  hold  regarding  the  nature  of 
any  of  the  virtues ;  he  rather  made  them  partners 
in  an  investigation,  and  by  means  of  skilful  questions 
tried  to  assist  them  in  discovering  the  real  nature  of 
goodness  for  themselves.  Another  point  to  be  noticed 
is  that  the  definition  of  the  various  virtues  was  reached 


22  DEVELOPMENT  OF  LOGIC 

as  a  result  of  comparing  the  views  of  a  number  of 
individuals.  In  this  way,  by  comparing  the  opinions 
of  many  men,  of  different  professions,  and  of  different 
grades  of  society,  he  was  able  to  separate  what  was 
merely  individual  and  relative  in  these  opinions,  from 
what  was  unchanging  and  absolute. 

Plato,  the  disciple  of  Socrates,  continued  the  work 
of  his  master.  He  did  not  confine  his  attention  wholly 
to  the  moral  conceptions,  but  showed  that  the  Socratic 
method  could  also  be  used  to  refute  the  intellectual  scep- 
ticism of  the  Sophists.  In  other  words,  he  proved  that 
in  the  concept,  or  thought,  as  opposed  to  sensation,  a 
standard  of  truth  is  to  be  found,  as  well  as  a  standard 
of  morality.  Knowledge  arises  from  thinking,  and  it 
is  possible  to  compare  our  thoughts,  however  impossi- 
ble it  may  be  to  find  any  basis  of  comparison  in  our 
sensations. 

Plato's  disciple^Aristotle,  is  of  great  importance  in 
the  history  of  logic.  He  undertook  a  thorough  investi- 
gation of  the  process  of  reasoning,  and  sought  to  show 
what  conditions  and  principles  are  necessarily  involved 
in  reaching  certainty.  Aristotle  was  thus  the  founder  of 
logic,  as  well  as  of  psychology,  zoology,  and  a  number 
of  other  sciences.  His  most  important  logical  works 
are  the  Categories •,  De  Interpretation,  Prior  Analytics, 
Posterior  Analytics,  Topics,  and  the  Sophistical  Elenchus, 
a  treatise  on  Fallacies.  These  writings  came  after- 
wards to  be  known  as  the  Organon  (or  scientific  instru- 
ment) of  Aristotle.  They  contained,  in  the  first  place, 
what  we  call  theory  of  knowledge  (a  discussion  of  the 
structure  of  knowledge,  and  of  the  scientific  principles 
r\ 


§  5.  THE  LOGIC  OF  THE  GREEKS        .  23 

upon  which  it  rests),  which  formed  an  essential  part  of 
Aristotle's  philosophical  system.  But  they  also  fur- 
nished the  practical  application  of  these  principles.  In 
his  doctrine  of  the  syllogism,  which  is  found  mainly  in 
the  Prior  Analytics,  he  showed  what  are  the  only  valid 
forms  of  reasoning,  and  thus  furnished  the  pattern  or 
type  to  which  all  proofs  must  conform.  He  also  classi- 
fied, in  his  work  on  Fallacies,  the  various  species  of 
false  reasoning ;  and  showed  how  false  arguments  could 
be  refuted  and  exposed  by  the  principles  which  he  had 
discovered.  The  form  to  which  Aristotle  maintained  that 
all  true  reasoning  can  be  reduced  was  as  follows  :  — 

All  men  are  mortal, 
Socrates  is  a  man, 
Therefore  Socrates  is  mortal. 

This  is  called  a  Syllogism,  and  it  is  made  up  of  three 
propositions.  The  first  two  propositions  are  called 
Premises,  and  the  last  the  Conclusion.  Every  piece  of 
reasoning,  all  proof,  can  be  reduced  to  this  form.  Of 
course,  the  propositions  which  make  up  the  syllogism 
do  not  always  stand  in  this  order,  and  sometimes  one  of 
them  may  be  omitted.  Thus  in  the  argument :  '  he 
ought  to  be  supported  by  the  state,  for  he  is  an  old 
soldier/  the  conclusion  stands  first,  and  one  premise  is 
wanting  entirely.  It  is  easy  to  see,  however,  that  the 
real  argument  when  properly  arranged  is  equivalent  to 
this :  - 

All  old  soldiers  ought  to  be  supported  by  the  state, 

He  is  an  old  soldier, 

Therefore  he  ought  to  be  supported  by  the  state. 

Now  the  part  of   Aristotle's  logic  which  was   best 


24  DEVELOPMENT  OF   LOGIC 

worked  out,  was  a  theory  of  proof  or  demonstration  b) 
means  of  the  syllogism.  Here  he  showed  clearly  the 
various  ways  in  which  different  kinds  of  propositions 
could  be  combined  as  premises  to  yield  valid  conclu- 
sions, and  proved  that  no  conclusion  could  be  drawn 
from  other  combinations.  This  part  of  the  Aristotelian 
logic  has  come  down  to  us  almost  unchanged,  and  is 
the  subject  of  Part  I.  of  the  present  volume. 

It  will  be  noticed  that,  in  the  doctrine  of  the  syllogism, 
Aristotle  was  dealing  with  that  kind  of  reasoning  which 
undertakes  to  demonstrate  the  truth  of  some  fact, 
by  showing  its  relation  to  a  general  principle  which 
every  one  admits.  In  other  words,  this  part  of  his 
work  may  be  called  the  logic  of  proof  or  demonstra- 
tion. Aristotle  was  at  one  time  of  his  life  a  teacher  of 
rhetoric,  and  he  seemed  always  to  have  aimed  at  putting 
this  art  of  reasoning  on  a  scientific  basis.  That  is,  for 
the  rules  of  thumb  and  questionable  artifices  of  the 
Sophists,  he  wished  to  substitute  general  laws  and 
methods  of  procedure  which  were  based  upon  a  study 
of  the  principles  and  operations  of  reason.  By  com- 
plying with  the  rules  which  he  laid  down,  an  argument 
will  necessarily  gain  the  assent  of  every  rational  being. 

But  we  do  not  employ  our  reason  merely  in  order  to 
demonstrate  to  ourselves  or  to  others  what  we  already 
know.  We  seek  to  discover  new  facts  and  truths  by 
its  aid.  In  other  words,  we  not  only  wish  to  prove  what 
is  already  known,  but  also  to  discover  new  facts,  and  we 
need  a  logic  of  Discovery,  as  well  as  a  logic  of  Proof. 
This  distinction  between  proof  and  discovery  corre- 
sponds in  general  to  that  between  Deduction  and  In- 


§  5.    THE  LOGIC  OF  THE  GREEKS  25 

duction.  Deduction  is  the  process  of  showing  how 
particular  facts  follow  from  some  general  principle  which 
everybody  admits,  while  Induction  shows  the  methods 
by  which  general  laws  are  obtained  from  an  observation 
of  particular  facts.  Now  Aristotle,  as  we  have  seen, 
furnished  a  very  complete  theory  of  Deduction,  or 
method  of  proof.  But  he  did  not  treat  of  Induction, 
or  the  method  of  passing  from  particular  facts  to  gen- 
eral laws,  with  anything  like  the  same  completeness. 
Moreover,  what  he  did  write  on  this  subject  received  no 
attention  for  many  centuries.  Aristotle  was  himself  a 
great  scientific  observer,  and  may  well  be  regarded  as 
the  father  of  the  natural  history  sciences.  But,  in  his 
logical  writings,  his  main  object  seems  to  have  been  to 
present  a  true  theory  of  argumentation,  as  opposed  to 
the  false  theories  of  the  Sophists.  Science,  too,  was 
only  in  its  beginning  when  Aristotle  wrote,  and  it  was 
impossible  for  him  to  foretell  the  methods  of  discovery 
which  it  has  actually  employed. 

After  Aristotle's  death  (322  B.C.),  and  after  the  loss 
of  Athenian  independence,  there  was  a  great  decline  of 
interest  in  matters  of  mere  theory  which  had  no  direct 
application  to  the  practical  affairs  of  life.  The  Stoic 
school  did  make  some  slight  additions  to  logical  theory, 
but  like  their  opponents,  the  Epicureans,  they  regarded 
practice,  the  art  of  living  well,  as  the  supreme  wisdom 
of  life.  The  Romans,  who  derived  their  knowledge  of 
Greek  philosophy  largely  from  the  Stoics,  were  also  in- 
terested in  the  practical  advantages  of  logic,  rather  than 
in  its  theoretical  side.  It  was  the  possibility  of  apply- 
ing the  laws  of  logic  to  rhetoric  and  public  speaking 


26  DEVELOPMENT  OF   LOGIC 

which  especially  interested  Cicero,  who  was  the  first  to 
make  Latin  paraphrases  and  adaptations  of  Greek  logic 
in  his  rhetorical  works. 

§  6.  Logic  during  the  Middle  Ages.  —  For  more  than 
seven  hundred  years,  during  the  Middle  Ages,  the  Greek 
language  and  literature  was  almost  unknown  in  Western 
Europe.  During  this  time,  almost  the  only  sources  of 
information  regarding  logic  were  Latin  translations  of 
Aristotle's  Categories,  and  of  an  Introduction  to  the  same 
work  by  Porphyry,  who  lived  232-303  A.D.  Both  of  these 
translations  were  made  by  Boethius  (470-525),  who  is  best 
known  as  the  author  of  The  Consolations  of  Philosophy. 
Even  when  scholars  again  became  acquainted  with  the 
original  works  of  Aristotle,  in  the  latter  part  of  the 
Middle  Ages,  they  did  not  really  understand  their  true 
significance.  They  took  the  husk,  one  may  say,  and 
neglected  the  kernel.  They  adopted  the  Aristotelian 
logic  as  an  external  and  arbitrary  set  of  rules  for  the 
guidance  of  thinking,  and  neglected  entirely  the  sci- 
entific theory  upon  which  these  rules  were  based.  A 
great  deal  of  ingenuity  was  also  shown  in  subdividing 
and  analyzing  all  possible  kinds  of  argument,  and  giv- 
ing the  particular  rule  for  each  case.  This  process  of 
making  distinctions  was  carried  so  far  that  scholastic 
logic  became  extremely  cumbersome  and  artificial.  Its 
pretensions,  however,  rapidly  increased;  it  claimed  to 
furnish  a  complete  instrument  of  knowledge,  and  a  sure 
standard  for  discriminating  between  truth  and  false- 
hood. 

It  is  not  very  difficult  to  understand  why  this  set  of  logical  rules 


§  6.     LOGIC  DURING  THE  MIDDLE  AGES  27 

seemed  so  satisfactory  to  the  age  of  Scholasticism.  The  men  of  this 
period  had  no  desire  to  increase  their  knowledge;  they  supposed 
that  they  were  already  in  possession  of  everything  which  was  worth 
knowing.  Their  only  object  was  to. weave  this  knowledge  into  a 
system,  to  show  the  connection  and  interdependence  of  all  its  parts, 
and  thus  to  put  it  "beyond  the  possibility  of  attack.  And  for  this 
purpose,  the  school  logic  was  admirably  adapted ;  it  was  always 
possible  to  bring  every  case  which  could  arise  under  one  or  other  of 
its  rules. 

There  is  no  doubt  that  the  Aristotelian  logic  had 
a  real  value  of  its  own,  and  that  it  exercised  a  very 
important  influence  upon  Western  civilization,  even  in 
the  form  in  which  it  was  taught  by  the  Schoolmen; 
but  there  is,  of  course,  nothing  complete  or  final  about 
it.  Its  main  purpose,  as  we  have  already  seen,  was  to 
furnish  a  method  by  means  of  which  the  knowledge  we 
already  possess  may  be  so  arranged  as  to  be  absolutely 
convincing.  But  the  centre  of  intellectual  interest  has 
changed  since  mediaeval  times.  We  are  not  content 
merely  to  exhibit  the  certainty  and  demonstrative  char- 
acter of  the  knowledge  which  we  already  have,  but  we 
feel  that  there  is  a  great  deal  of  importance  still  to  be 
discovered.  So  that,  in  modern  times,  one  may  say  the 
desire  to  make  discoveries,  and  so  add  to  the  general 
stock  of  knowledge,  has  taken  the  place  of  the  medi- 
aeval ideal  of  showing  that  the  traditional  doctrines 
taught  by  the  church  are  absolutely  certain  and  con- 
vincing. And  when  men  became  conscious  of  the 
importance  of  gaining  new  knowledge,  and  especially 
knowledge  about  nature,  they  at  once  saw  the  neces- 
sity for  a  new  logic,  or  doctrine  of  method,  to  aid  them 
in  the  undertaking. 


28  DEVELOPMENT  OF   LOGIC 

§  7.  The  Logic  of  Bacon.  —  All  the  great  thinkers 
of  the  sixteenth  and  seventeenth  centuries  saw  clearly 
that  the  school  logic  is  simply  a  method  of  showing  the 
certainty  of  the  knowledge  we  already  possess,  and 
does  not  aid  us  at  all  in  making  new  discoveries.  A 
new  method,  they  all  declared,  was  an  absolute  neces- 
sity. The  new  point  of  view  was  put  most  clearly  and 
eloquently  by  the  famous  Francis  Bacon  (1561-1626), 
at  one  time  Lord  Chancellor  of  England.  Bacon  called 
his  work  on  logic  the  Novum  Organum,  thus  contrast- 
ing it  with  the  Organon,  or  logical  treatises  of  Aristotle. 
An  alternative  title  of  the  work  is,  True  Suggestions  for 
the  Interpretation  of  Nature.  Bacon  begins  this  work 
by  showing  the  advantages  to  be  gained  from  a  know- 
ledge of  nature.  It  is  man's  true  business,  he  tells  us, 
to  be  the  minister  and  interpreter  of  nature,  for  it  is  only 
by  becoming  acquainted  with  the  laws  of  nature  that  we 
are  ever  able  to  "take  advantage  of  them  for  our  own 
ends.  "  Knowledge  and  human  power  are  synonymous, 
since  ignorance  of  the  cause  prevents  us  from  taking 
advantage  of  the  effect."  The  discovery  of  the  laws  of 
nature,  which  is  therefore  of  so  great  practical  impor- 
tance, cannot  be  left  to  chance,  but  must  be  guided  by 
a  scientific  method.  And  it  is  such  a  method  which 
Bacon  endeavours  to  supply  in  the  Novum  Organum. 

The  method  which  Bacon  proposed  seems  to  us  very 
simple.  If  we  would  gain  new  knowledge  regarding 
nature,  he  says,  and  regarding  natural  laws,  we  must 
go  to  nature  herself  and  observe  her  ways  of  acting. 
Facts  about  nature  cannot  be  discovered  from  logical 
propositions,  or  from  syllogisms ;  if  we  would  know  the 


§  8.     LOGIC  SINCE  THE  TIME  OF  BACON  2Q 

law  of  any  class  of  phenomena,  we  must  observe  the  par- 
ticular facts  carefully  and  systematically.  It  will  often 
be  necessary,  also,  to  put  pointed  questions  to  nature 
by  such  experiments  as  will  force  her  to  give  us  the 
information  we  want.  Knowledge,  then,  must  begin 
with  observation  of  particular  facts ;  and  only  after  we 
have  made  a  great  number  of  particular  observations, 
and  have  carefully  classified  and  arranged  them,  taking 
account  of  all  the  negative  cases,  are  we  able  to  discover 
in  them  the  general  law.  No  hypotheses  or  guesses  are 
to  be  made  ;  but  we  must  wait  until  the  tabulations  of 
the  particular  phenomena  reveal  the  general  '  form  '  or 
principle  which  belong  to  them  all. 

It  will  be  frequently  necessary  to  refer  to  Bacon's 
work  in  what  follows.  At  present,  it  is  sufficient  to 
note  thatn  Bacon  showed  that  a  knowledge  of  nature 
cannot  be  attained  through  general  propositions  and 
logical  arguments,  but  that  it  is  necessary  to  begin 
with  the  observation  of  particular  facts.1  He  empha- 
sized, also, .  the  importance  of  systematic  observation 
and  carefully  planned  experiments,  and  showed  that 
knowledge  must  begin  with  facts  of  perception.  This 
is  the  method  of  induction,  and  Bacon  is  usually  said 
to  have  been  the  founder  of  the  inductive  sciences  of 
nature. 

§  8.  Logic  since  the  Time  of  Bacon.  —  Another  and 
quite  different  method  of  extending  knowledge  was  pro- 
posed by  the  great  Frenchman,  Descartes  (1596-1650), 
who  took  mathematics  as  the  type  to  which  all  know- 
ledge should  conform.  That  is,  he  supposed  that  the 


3O  DEVELOPMENT  OF  LOGIC 

true  method  of  extending  knowledge  was  to  begin  with 
general  principles,  whose  truth  could  not  be  doubted, 
and  to  reason  from  them  to  the  necessary  character 
of  particular  facts.  Descartes  and  his  followers  thought 
that  it  was  possible  to  discover  certain  axiomatic  propo- 
sitions from  which  all  truth  could  be  derived  through 
reason.  They  thus  emphasized  Deduction  rather  than 
Induction,  and  reasoning  rather  than  observation  and 
experiment.  The  spirit  of  Bacon's  teaching  was,  how- 
ever, continued  in  England  by  John  Locke,  in  the 
Essay  Concerning  Human  Understanding  (1690).  Dur- 
ing the  next  centuries,  philosophical  thinkers  were 
divided  into  two  great  schools,  —  Rationalists,  or  those 
who  agreed  in  the  main  with  Descartes,  and  Empiricists, 
or  Sensationalists,  who  followed  the  teachings  of  Bacon 
and  Locke. 

Although  the  natural  sciences  made  great  advances 
during  the  seventeenth  and  eighteenth  centuries,  there 
seems  to  have  been  no  effort  made  to  analyze  and 
describe  the  methods  which  were  actually  being  em- 
ployed. In  England,  at  least,  it  seems  to  have  been 
assumed  that  all  discoveries  were  made  by  the  use  of 
the  rules  and  methods  of  Bacon.  One  of  the  first 
writers  to  attempt  to  explain  the  method  used  by  the 
natural  sciences  was  Sir  John  Herschel  (1792-1871). 
His  work,  Discourse  on  the  Study  of  Natural  Philosophy, 
was  published  in  1832.  A  little  later,  and  with  the 
same  object  in  view,  William  Whewell  (1794-1866), 
afterwards  Master  of  Trinity  College,  Cambridge,  un- 
dertook his  History  of  the  Inductive  Sciences,  which 
was  followed  some  time  after  by  the  Philosophy  of  the 


§  8.     LOGIC  SINCE  THE  TIME  OF  BACON  3 1 

Inductive  Sciences.  The  man,  however,  who  did  most 
towards  putting  the  study  of  logic  on  a  new  basis  was 
John  Stuart  Mill  (1806-1873),  the  first  edition  of  whose 
Logic  appeared  in  1843.  We  shall  have  frequent  occa- 
sion to  refer  to  this  work  in  future  discussions.  It  is 
sufficient  to  say  here  that  Mill  continues  the  empirical 
tradition  of  the  earlier  English  writers  in  his  general 
philosophical  position.  Mill's  book  gave  a  great  im- 
pulse to  the  study  of  logic.  Before  it  was  published, 
writers  on  the  subject  had  confined  their  attention 
almost  exclusively  to  the  syllogistic  or  deductive  rea- 
soning. Mill,  however,  emphasized  strongly  the  impor- 
tance of  induction ;  indeed,  he  regarded  induction  as 
the  only  means  of  arriving  at  new  truth,  deduction 
being  merely  a  means  of  systematizing  and  arranging 
what  we  already  know.  Though  few  logicians  of  the 
present  day  adopt  this  extreme  view,  the  importance  of 
inductive  methods  of  reasoning,  and  the  necessity  of 
studying  them,  have  now  become  generally  recognized. 
Most  modern  writers  on  logic  devote  a  considerable 
amount  of  attention  to  induction.  The  reader  will  find 
that  Part  II.  of  the  present  volume  deals  with  this 
subject. 

There  is  still  another  side  of  logic  which  has  been 
developed  in  the  English-speaking  world  since  the  time_  ' 
of  Mill,  though  it  is  a  direct  continuation  of  the  move- 
ment started  in  Germany  by  Kant  more  than  a  hun- 
dred years  ago.  The  so-called  '  modern '  logic  has  laid 
aside  the  formalism  and  paradoxical  mode  of  expression 
adopted  by  Hegel,  but  the  fundamental  conceptions 
with  which  it  works  are  essentially  the  same  as  those 


32  DEVELOPMENT  OF   LOGIC 

employed  by  the  latter  in  his  Wissenschaft  der  Logik 
(1816-1818).  It  has  been  within  the  last  twenty  years 
that  the  results  of  German  idealism  —  the  doctrines  of 
Kant,  Fichte,  Schelling,  and  Hegel  —  have  become 
naturalized  in  England  and  America.  And  largely  as 
a  consequence  of  these  teachings,  a  new  conception  of 
the  nature  of  thought  has  grown  up,  and  given  rise  to 
investigations  which  may  be  said  to  have  created  a 
'  modern '  logic  that  is  fairly  entitled  to  rank  beside 
its  sister  science,  the  '  new '  psychology. 

The  Aristotelian  doctrine  of  the  syllogism  is  a  purely 
formal  science.  In  the  form  in  which  it  is  represented 
in  ordinary  text-books,  it  might  perhaps  be  more  prop- 
erly described  as  the  art  of  arranging  our  knowledge 
in  such  a  way  as  to  compel  assent.  The  '  matter '  with 
which  thought  is  supposed  to  work  is  supplied  to  it  in 
form  of  concepts  and  judgments.  The  problem  which 
formal  logic  has  to  solve  is  to  define  and  classify  the 
various  kinds  of  concepts  with  which  thought  operates, 
and  to  determine  the  various  relations  in  which  these 
stand  when  combined  into  judgments.  Similarly,  it 
has  to  show  what  combinations  of  judgments  can  be 
employed  as  premises  leading  to  valid  conclusions  in 
the  syllogism.  The  criterion  of  truth  employed  in  these 
investigations  is  the  principle  of  non-contradiction  or 
consistency.  Inconsistent  combinations  of  concepts, 
that  is,  are  ruled  out ;  but  so  far  as  the  doctrine  of 
the  syllogism  goes,  anything  is  true  which  is  not  self- 
contradictory. 

Now,  without  questioning  the  practical  value  of  its 
canons,  it  is  obvious  that  formal  or  syllogistic  logic  does 


§  8.    LOGIC   SINCE  THE  TIME  OF  BACON  33 

not  take  any  account  of  many  of  the  processes  of  every- 
day thought,  and  that  its  rules  go  but  a  little  way  in 
helping  us  to  distinguish  the  true  from  the  false.  For, 
in  the  first  place,  to  think  is  not  merely  to  combine  and 
arrange  ideas  already  in  our  possession.  This  might 
enable  us  to  render  clearer  and  more  definite  what  we 
already  know,  but  would  never  enable  us  to  gain  new 
knowledge.  The  real  movement  of  thought  —  as  op- 
posed to  its  merely  formal  procedure  —  consists  in  the 
formation  of  new  ideas  and  new  knowledge  through 
actual  contact  with  the  world  of  experience.  (A  com- 
plete account  of  the  intellectual  process,  then,  must 
/deal  with  the  relation  of  the  mind  to  objects;  it  must 
^investigate  the  various  activities  by  means  of  which 
thought  interprets  the  world  and  builds  up  the  various 
sciences  of  nature  and  of  man/) 

The  recognition  of  the  importance  of  induction,  and 
of  the  necessity  of  studying  the  methods  of  the  induc- 
tive sciences  which  was  brought  about  by  Whewell, 
Mill,  and  others,  was  a  step  in  the  right  direction,  for 
it  called  attention  to  a  kind  of  thinking  which  occupies 
a  large  place  in  our  intellectual  life,  and  also  gave  rise 
to  a  truer  conception  of  the  nature  of  thought  itself. 
But  even  Mill  did  not,  reach  the  idea  which  guides 
modern  logicians,  that  thought  or  intelligence  is  one 
from  beginning  to  end,  and  that  the  various  logical 
processes  are  all  parts  of  one  whole,  or  rather  ways  in 
which  intelligence  operates  in  different  circumstances, 
or  at  different  stages  of  its  development.  He  still 
treats  of  logical  processes,  like  conception,  judgment, 
and  reasoning,  as  if  they  were  quite  separate  from 


34  DEVELOPMENT  OF   LOGIC 

each  other;  and,  as  has  already  been  noticed,  in  his 
zeal  for  induction,  he  fails  completely  to  do  justice  to 
syllogistic  reasoning. 

As  opposed  to  the  division  of  mind  into  separate 
faculties,  the  thought  by  which  modern  logic  is  domi- 
nated is  that  of  the  unity  and  continuity  of  all  intel- 
lectual life.  Thought  is  regarded  as  an  organic,  living 
function  or  activity,  which  remains  identical  with  itself 
throughout  all  its  developing  forms  and  phases.  The 
problem,  accordingly,  which  logic  must  set  before  itself 
is  to  show  the  unity  and  interrelation  of  all  of  the 
intellectual  processes.  No  one  of  the  steps  or  stages 
in  this  process  can  be  completely  understood  when 
viewed  by  itself :  each  is  what  it  is  only  in  and  through 
its  connection  with  the  whole  of  which  it  forms  a  part: 
No  hard  and  fast  boundary  lines  are  to  be  drawn  be- 
tween the  different  stages  of  the  reasoning  process,  but 
it  must  be  shown  that  the  whole  nature  of  intelligence 
is  involved  more  or  less  explicitly  at  each  step.  So 
far  only  the  broad  outlines  of  this  theory  have  been 
filled  in ;  but  the  conception  of  an  organism  whose 
parts  are  developing  in  mutual  relation  and  inter- 
dependence, promises  to  be  as  fruitful  when  applied 
to  logic  as  it  has  already  shown  itself  to  be  in  the 
other  sciences. 

Besides  the  ordinary  histories  of  philosophy  the  reader  may  con- 
sult for  the  history  of  logic  :  Prantl,  Geschichte  der  Logik  im  Abend- 
lands,  4  vols.,  Leipsic,  1855-1870;  which  extends,  however,  only  to 
the  close  of  the  mediaeval  period.  Harms,  Geschichte  der  Logik, 
Berlin,  1881.  Ueberweg,  System  der  Logik,  4th  ed.,  1874;  Eng. 
trans,  of  3d  ed.,  London,  1874.  Adamson,  article  *  Logic,1  in  the 


§  8.     LOGIC   SINCE  THE  TIME  OF  BACON  35 

Encyl.  Brit.,  gth  ed.  Sir  William  Hamilton's  Lectures  on  Logic, 
also  contain  much  historical  information. 

Among  modern  works  on  logic,  the  following  may  be  mentioned  : 
J.  S.  Mill,  A  System  of  Logic,  London,  ist  ed.,  1843  ;  Qth  ed.,  1875. 
W.  S.  Jevons,  The  Principles  of  Science,  London,  1874;  2d  ed., 
1877.  Also,  by  the  same  author,  Studies  in  Deductive  Logic,  1880; 
and  Piire  Logic,  1890.  H.  Lotze,  Logik,  1874;  Eng.  trans.,  Lon- 
don, 1881  and  1888.  W.  Wundt,  Logik,  2d  ed.,  1896.  C.  Sigwart, 
Logik,  2d  ed.,  1889-1893  ;  Eng.  trans.,  London  and  New  York,  1895. 

The  newer  development  of  logic  is  well  represented  by  F.  H.  Brad- 
ley,  The  Principles  of  Logic,  London,  1886.  B.  Bosanquet,  Logic, 
or  the  Morphology  of  Knowledge,  London,  1888  ;  and  The  Essentials 
of  Logic,  London  and  New  York,  1895.  L.  T.  Hobhouse,  The  Theory 
of  Knowledge,  London,  1896,  may  also  be  mentioned  in  the  same 
group  of  writers,  although  he  has  been,  perhaps,  more  influenced  by 
Mill  than  by  any  other  writer. 

The  following  works,  among  others,  have  proved  useful  as  text- 
books :  W.  S.  Jevons,  Elementary  Lessons  in  Logic,  London  and 
New  York,  1870.  A.  Bain,  Logic,  Deductive  and  Inductive,  New 
York,  1883.  J.  H.  Hyslop,  The  Elements  of  Logic,  New  York,  1892. 
W.  Minto,  Logic  Inductive  and  Deductive,  New  York,  1894.  J.  G. 
Hibben,  Inductive  Logic,  New  York,  1896. 

C,'. 


' 


PART    I.  — THE   SYLLOGISM 
CHAPTER   III 

THE  SYLLOGISM  AND  ITS  PARTS 

§9.  The  Nature  of  the  Syllogism. — The  theory  of 
the  syllogism,  as  has  been  already  stated  (§5),  was 
first  worked  out  by  Aristotle.  And  it  stands  to-day 
in  almost  the  same  form  in  which  he  left  it.  A  few 
additions  have  been  made  at  different  points,  but  these 
do  not  affect  materially  the  main  doctrine.  In  deal- 
ing with  the  nature  of  the  syllogism,  we  shall  first 
try  to  understand  its  general  aim  and  purpose,  or  the 
results  which  it  seeks  to  bring  about.  We  shall  then 
have  to  analyze  it  into  the  parts  of  which  it  is  com- 
posed, and  to  examine  and  classify  the  nature  of  these 
elements.  Finally,  it  will  be  necessary  to  discover 
what  rules  must  be  observed  in  order  to  obtain  valid 
conclusions,  and  to  point  out  the  conditions  which 
most  commonly  give  rise  to  error  or  fallacy. 

In  the  first  place,  it  is  to  be  noticed  that  syllogistic 
logic  deals  with  the  results  of  thinking,  rather  than 
with  the  nature  of  the  thought-process.  Its  object  is 
not  to  give  an  account  of  the  way  in  which  thinking 
goes  on,  but  to  show  how  the  ideas  and  thoughts  which 
we  already  possess  may  be  combined  so  as  to  compel 

36 


§  9.     THE  NATURE  OF  THE  SYLLOGISM  37 

assent.  The  ideas  which  it  uses  as  material  are  fixed 
by  having  been  expressed  in  language.  Indeed,  it  is 
largely  with  words,  as  the  expression  of  thoughts,  that 
syllogistic  logic  deals.  Many  of  the  discussions  with 
which  it  is  occupied  have  reference  to  the  meanings 
of  words  and  propositions ;  and  the  rules  which  it  fur- 
nishes may  be  taken  as  directions  for  putting  together 
propositions  in  such  a  way  as  to  lead  to  a  valid  conclu- 
sion. Nevertheless,  it  is  important  to  remember  that 
these  rules  are  not  arbitrary  and  external,  but  find  their 
justification  in  the  nature  of  thought.  Indeed,  the 
theory  of  the  syllogism,  when  rightly  understood,  may 
be  said  to  reveal  the  fundamental  characteristics  of  the 
process  of  intelligence.  For  it  brings  together  facts 
in  such  a  way  as  to  make  evident  their  relation  and 
dependence.  It  connects  a  judgment  with  the  grounds 
or  reasons  which  support  it,  and  is  thus  a  process  of 
systematization.  In  order  to  understand  the  signifi- 
cance of  the  rules  of  syllogistic  logic,  then,  it  will 
frequently  be  necessary  to  look  beyond  words  and 
propositions  to  the  act  of  thought  whose  result  they 
express. 

A  great  deal  has  been  written  regarding  the  princi- 
ples, or  laws  of  thought,  which  are  employed  in  syllo- 
gistic reasoning.  It  seems  better,  however,  to  postpone 
the  definite  consideration  of  this  subject  until  the  student 
has  learned  more  about  the  various  kinds  of  syllogisms, 
and  has  had  some  practice  in  working  examples.  In 
dealing  with  the  nature  and  principles  of  thought  in  the 
third  part  of  this  book,  it  will  be  necessary  to  discuss 
this  question  at  length.  Even  at  the  present  stage  of 


38  THE   SYLLOGISM   AND   ITS   PARTS 

our  inquiry,  however,  it  is  important  to  notice  that  syl- 
logistic reasoning  presupposes  certain  simple  and  fun- 
damental principles  of  thought  whose  nature  we  shall 
have  to  examine  hereafter.  In  particular,  the  regular 
syllogism  is  founded  on  a  principle  which  we  may  call 
/the  law  of  Identity,  or  the  law  of  Contradiction^  according 
as  it  is  stated  affirmatively  or  negatively.  Stated  affirm- 
atively, this  so-called  '  law '  simply  expresses  the  fact 
that  every  term  and  idea  which  we  use  in  our  reason- 
ings must  remain  what  it  is.  A  is  A,  or  has  the  same 
value  and  meaning  wherever  employed.  The  law  of 
Contradiction  expresses  the  same  thing  in  negative 
language.  A  cannot  be  both  B  and  not  B.  If  any 
term  is  taken  to  be  the  same  as  another  in  one  connec- 
tion, it  must  always  be  taken  to  be  so ;  if  it  is  different, 
this  relation  must  everywhere  be  maintained.  The 
data  or  materials  which  are  employed  in  the  syllogism 
are  ideas  whose  meaning  is  supposed  to  be  perma- 
nently fixed,  and  expressed  in  words  which  have  been 
carefully  defined.  It  would  be  impossible  to  reason,  or 
to  determine  the  relation  of  our  ideas,  if  their  mean- 
ing were  to  change  without  notice,  or  if  the  words  by 
means  of  which  they  are  expressed  were  used  now  in 
one  sense,  and  now  in  another.  It  is  of  course  true 
that  our  ideas  regarding  the  nature  of  things  change 
from  time  to  time/  And,  as  is  evident  from  one's  own 
experience,  as  well  as  from  the  history  of  language,  a 
corresponding  change  takes  place  in  the  meaning  of 
words.  But  the  assumption  upon  which  syllogistic 
reasoning  proceeds,  is  that  the  ideas  which  are  to  be 
compared  are  fixed  for  the  mean  time,  and  that  the 


§  io.    THE   PARTS  OF  A   SYLLOGISM  39 

words  by  which  they  are  expressed  are  used  in  the 
same  sense  throughout  the  course  of  the  argument. 
In  this  kind  of  reasoning,  then,  just  as  in  geometry,  it 
is  essential  that  the  terms  which  enter  into  the  argu- 
ment be  clearly  and  precisely  defined,  and  that  when 
thus  determined  they  shall  be  taken  as  fixed  and  un- 
changeable until  further  notice  is  given. 

It  is  quite  possible  that  all  the  requirements  of  the 
syllogism  may  be  met  without  its  conclusions  being 
true  of  reality.  In  other  words,  an  argument  may  be 
formally  true,  but  really  false.  It  is  not  difficult  to 
understand  why  this  may  happen.  The  syllogism  ac- 
cepts the  ideas  and  judgments  which  it  compares  with- 
out criticism.  These  data  are  of  course  the  product  of 
previous  acts  of  thinking.  But  in  proceeding  to  ar- 
range them  in  syllogistic  form,  we  do  not  inquire 
whether  or  not  they  are  true;  i.e.  adequate  to  express 
the  nature  of  the  things  for  which  they  stand.  For 
the  purposes  of  the  syllogism  it  is  only  essential  that 
their  meanings  be  clearly  understood,  and  that  these 
meanings  be  regarded  as  fixed  and  permanent. 

§  io.  The  Parts  of  a  Syllogism. — The  syllogism  may 
be  said  to  express  a  single  comprehensive  act  of  thought. 
We  may  define  inference  as  a  judgment  which  has  been 
expanded  so  as  to  exhibit  the  reasons  by  which  it  is 
supported.  In  the  syllogism 

The  geranium  has  five  pointed  sepals, 
This  plant  has  not  five  sepals, 
Therefore  it  is  not  a  geranium. 

we  may  say  that  we  have  the  judgment,  'this  plant  is 


40  THE  SYLLOGISM   AND   ITS   PARTS 

not  a  geranium,'  supported  by  the  propositions  which 
precede  it,  and  that  the  whole  syllogism  taken  together 
expresses  a  single  thought,  which  is  complete  and  self- 
sufficient.  It  is  possible,  however,  even  when  one  is 
dealing  directly  with  the  process  of  thinking,  to  dis- 
tinguish in  it  different  subordinate  steps,  various  stages 
which  serve  as  resting  places,  in  the  course  of  its  passage 
to  the  complete  and  comprehensive  form  represented 
by  the  syllogism.  But  it  is  usual,  in  dealing  with  the 
syllogism,  to  take  a  more  external  view  of  its  nature, 
and  to  regard  it  primarily  as  made  up  of  words  and 
propositions. 

In  this  sense,  a  syllogism  can,  of  course,  be  divided 
into  parts.  In  the  first  place,  it  is  composed  of  three 
propositions.  In  the  example  given  above  the  two 
propositions  which  stand  first  are  called  the  premises, 
since  they  furnish  the  grounds  or  reasons  for  the  propo- 
sition which  stands  last,  and  which  is  known  as  the 
conclusion.  However,  it  is  not  true  that  we  always 
find  the  two  premises  and  the  conclusion  arranged  in 
this  regular  order  in  syllogistic  arguments.  Oftentimes 
the  conclusion  is  given  first.  Frequently,  too,  one  of 
the  premises  is  not  expressed,  and  has  to  be  supplied  in 
order  to  complete  the  argument.  Thus  the  statement, 
'he  must  be  more  than  sixteen  years  of  age,  for  he 
attends  the  university,'  is  an  incomplete  syllogism. 
The  conclusion,  as  will  be  readily  seen,  stands  first. 
There  is  also  only  one  premise  expressed.  To  put  this 
statement  in  the  regular  syllogistic  form  we  have  to 
supply  the  missing  premise  and  arrange  it  as  fol- 
lows :  — 


§  io.    THE  PARTS  OF  A   SYLLOGISM  41 

All  students  of  the  university  are  more  than  sixteen  years  of  age, 

He  is  a  student  of  the  university, 

Therefore  he  is  more  than  sixteen  years  of  age. 

When  one  premise  of  an  argument  is  lacking,  the  name 
of  enthymeme  is  applied  to  it.  When  an  argument  is 
defective  in  this  way,  it  must  be  remembered  that  the 
missing  proposition  is  to  be  regarded  as  in  consciousness, 
though  not  expressed.  It  is  of  great  importance  to  form 
the  habit  of  making  clear  to  oneself  the  premises  by 
which  any  conclusion  claims  to  be  supported.  In  this 
way  groundless  assumptions  are  often  brought  to  light, 
and  the  weakness  of  an  argument  exposed.  Whenever 
words  like  'therefore,'  'for,'  'because,'  'it  follows,'  etc., 
are  used  in  their  proper  signification,  it  is  possible  to 
find  an  argument  composed  of  two  premises  and  a  con- 
clusion. But  one  must  not  allow  oneself  to  be  imposed 
upon  by  the  mere  words,  but  must  insist  on  understand- 
ing exactly  what  are  the  premises  in  the  case,  and  how 
the  conclusion  follows  from  them. 

It  is  possible  to  carry  the  division  of  a  syllogism  still 
further.  Every  logical  proposition  may  be  divided  into 
two  terms,  and  a  copula  or  connecting  link.  The  terms, 
which  are  the  extremes  of  the  proposition,  are  named 
the  subject  and  the  predicate.  Thus  in  the  proposition, 
'  the  fields  are  covered  with  snow,'  '  the  fields '  is  the 
subject,  'are,'  the  copula,  and,  'covered  with  snow,' 
the  predicate.  To  reduce  a  proposition  to  the  logical 
form  in  which  it  is  most  conveniently  treated,  it  is  neces- 
sary to  express  it  in  such  a  way  that  the  two  terms  are 
united  by  some  part  of  the  verb  'to  be,'  preferably  'is* 
or  '  are.'  Thus  the  sentence,  '  No  plant  can  grow  with- 


42  THE   SYLLOGISM   AND   ITS  PARTS 

out  light  and  heat,'  would  be  expressed  as  a  logical 
proposition  in  the  following,  or  some  similar,  form  :  '  No 
plant  is  an  organism  which  can  grow  without  light  and 
heat.'  '  Men  have  strong  passions,'  may  be  written, 
'  Men  are  beings  having  strong  passions.'  It  is  always 
well  to  reduce  a  sentence  to  some  such  form,  by  substi- 
tuting for  the  verb  of  predication  some  part  of  the  verb 
'to  be.' 

The  analysis  of  the  syllogism  gives  us  the  divisions 
under  which  it  is  convenient  to  treat  this  part  of  logic. 
We  shall  accordingly  deal  (i)  with  Terms,  (2)  with 
Propositions,  and  (3)  with  the  Syllogism  as  a  whole. 

These  divisions,  however,  are  only  made  for  the  sake 
of  convenience  in  treatment.  It  must  not  be  forgotten 
that  a  term  is  a  part  of  a  proposition.  To  understand 
the  nature  of  a  term,  it  is  necessary  to  consider  the 
part  which  it  plays  in  the  judgment  which  the  propo-. 
sition  expresses.  In  other  words,  the  function  of  the 
term,  rather  than  the  form  of  the  word  or  words  em- 
ployed, must  be  considered.  It  is,  of  course,  true  that 
we  naturally  and  commonly  use  certain  word  forms  to 
express  certain  kinds  of  ideas,  just  as  in  the  grammati- 
cal sentence  the  different  '  parts  of  speech '  —  nouns, 
verbs,  etc., — have  each  a  definite  and  comparatively 
permanent  function.  But  even  in  the  sentence,  it  is  the 
part  which  the  word  in  its  grammatical  function  plays, 
rather  than  its  form,  which  determines  whether  it  is  to 
be  classified  as  a  noun  or  an  adjective,  a  preposition  or 
a  conjunction.  In  dealing  separately  with  terms,  as  we 
propose  to  do  in  the  next  chapter,  we  shall  be  occupied 
to  a  large  extent  with  the  form  of  words  in  which  cer- 


§  ii.    PROPOSED   DIVISION  OF  MENTAL  OPERATIONS       43 

tain  kinds  of  ideas  are  usually  expressed.  But,  as  the 
same  word  or  group  of  words  may  be  used  for  different 
purposes,  it  will  be  necessary,  in  order  to  understand 
the  meaning  of  terms,  to  refer  frequently  to  the  various 
ways  in  which  they  are  used  in  a  proposition. 

The  same  difficulty  exists  when  propositions  are  con- 
sidered by  themselves,  the  relation  to  the  complete 
argument  of  which  they  form  a  part  being  thus  ig- 
nored. In  this  case,  however,  the  results  of  the  isola- 
tion are  not  so  apparent,  for  a  proposition  forms,  in 
a  certain  sense,  a  whole  by  itself.  It  is  the  expression 
of  a  judgment  which,  as  we  shall  see  later,  is  the  unitary 
process  of  thought.  It  has  thus  a  significance  of  its 
own,  as  expressing  a  more  or  less  complete  and  inde- 
pendent act  of  thought.  Nevertheless,  it  must  not  be 
forgotten  that  its  independence  and  completeness  are 
only  partial  and  relative.  A  single  proposition  cannot 
stand  alone.  Taken  strictly  by  itself,  a  proposition  is 
only  a  fragment.  In  order  to  make  it  intelligible,  it 
must  be  brought  into  relation  with  the  other  proposi- 
tions which  state  the  grounds  or  reasons  upon  which 
it  rests,  or  the  conclusion  which  it  helps  to  support. 
The  logical  nature  of  a  proposition  will,  therefore,  de- 
pend upon  its  function  in  an  argument,  and  in  treating 
of  propositions  this  fact  must  not  be  forgotten. 

§  ii.    The  Proposed  Division  of  Mental  Operations. — 

It  is  frequently  stated  in  text-books  on  logic  that  corre- 
sponding to  the  division  into  Terms,  Propositions,  and 
Syllogisms,  there  must  be  a  division  of  the  different  kinds 
of  thought,  or  of  operations  of  the  mind.  These  differ- 


44  THE   SYLLOGISM  AND   ITS  PARTS 

ent  operations  are  usually  called  Simple  Apprehension, 
Judgment,  and  Reasoning.  "The  first  of  these,  Simple 
Apprehension,  is  the  act  of  mind  by  which  we  merely 
become  aware  of  something,  or  have  a  notion,  idea,  or 
impression  of  it  brought  into  the  mind.  The  adjective 
simple  means  apart  from  other  things,  and  apprehension, 
the  taking  hold  by  the  mind.  Thus  the  name  or  term 
'  iron '  instantaneously  makes  the  mind  think  of  a  very 
strong  and  very  useful  metal,  but  does  not  tell  us  any- 
thing about  it,  or  compare  it  with  anything  else." 1 
Judgment,  the  account  continues,  is  an  entirely  dif- 
ferent action  of  mind,  and  comes  later  than  Simple 
Apprehension.  It  consists  in  comparing  two  notions 
or  ideas  derived  from  simple  apprehension  in  order  to 
ascertain  whether  they  agree  or  differ.  In  order  to 
judge,  we  must  have  two  notions  or  ideas  ready  in  the 
mind.  The  judgment  results  from  comparing  these, 
and  affirming  that  they  agree  or  do  not  agree.  In 
the  same  way,  having  already  made  judgments,  we 
can  combine  them  into  arguments  or  processes  of 
reasoning  by  a  new  and  still  different  activity  of  mind. 
Apprehension,  judgment,  and  reasoning  are  thus  sup- 
posed to  be  separate  and  distinct  mental  operations. 
It  is  true  that  the  later  forms  employ  as  their  mate- 
rial the  finished  products  of  the  earlier.  But  from  this 
point  of  view,  apprehension,  judgment,  and  reasoning 
simply  succeed  one  another.  The  real  unity  which 
belongs  to  these  operations  as  forms  of  intelligence  is 
not  set  forth. 

1  Jevons,  Lessons  on  Logic,  pp.  n,  12. 


§  ii.    PROPOSED   DIVISION   OF   MENTAL  OPERATIONS       45 

The  whole  of  Part  III.  of  the  present  book  may  be 
regarded  as  an  argument  against  this  point  of  view. 
We  shall  there  endeavour  to  show  that  thinking  is  not 
a  process  of  externally  joining  on  part  to  part,  but 
consists  in  a  development  or  expansion  of  knowledge 
from  within.  And,  in  particular,  we  shall  try  to  ex- 
hibit the  essential  unity  of  intellectual  processes  by 
whatever  name  they  may  be  called,  and  at  whatever 
stage  of  development  they  may  be  found.  Without 
anticipating  too  far  our  future  discussions,  we  may  point 
out  that  the  primary  process  of  thought  is  not  '  Simple 
Apprehension/  but  Judgment.  In  other  words,  it  is 
impossible  to  apprehend  or  passively  receive  ideas. 
'To  get  an  idea,'  or  to  understand  the  meaning  of  a 
term,  is  only  possible  when  the  mind  judges  or  inter- 
prets things  for  itself.  To  have  an  idea  or  concept 
of  anything,  then,  is  to  be  able  to  judge  more  or  less 
clearly  and  confidently  regarding  it.  I  have  an  idea 
of  'iron'  when  I  judge  that  it  is  'black'  and  'heavy' 
and  '  malleable.'  And  the  more  complete  and  exact  we 
can  make  our  judgments,  the  better  is  the  idea  or  appre- 
hension which  we  obtain  of  the  thing  in  question.  In- 
telligence or  thought  must  not  be  regarded  as  at  first 
merely  receptive.  It  does  not  begin  by  laying  hold  of 
separate  ideas  or  terms,  and  afterwards  call  in  judg- 
ment as  a  new  kind  of  process  to  bring  the  former  into 
relation.  But  it  is  from  the  first  a  systematizing  and 
relating  activity  which  proceeds  from  the  less  perfect 
to  the  more  perfect  form  of  judgment  (cf.  §§  73,  74). 


CHAPTER   IV 

THE    VARIOUS    KINDS    OF    TERMS 

§  12.  Singular,  General,  and  Collective  Terms.  —  A 
logical  term,  as  we  have  already  seen,  is  an  element  of 
a  proposition.  In  dealing  with  terms  apart  from  prop- 
ositions, we  shall  be  concerned  mainly  with  different 
classes  of  words  and  the  meanings  which  they  usually 
express.  It  will  be  impossible,  however,  to  fix  th£ 
meanings  of  terms  absolutely  without  reference  to  the 
way  in  which  they  are  used  in  propositions.  The  first 
division  which  we  have  to  notice  is  that  into  Singular  or 
Individual,  General,  and  Collective  terms. 

(i)  A  Singular  or  Individual  term  is  one  which  can 
be  applied  in  the  same  sense  to  but  a  single  thing. 
The  main  purpose  of  Singular  terms  is  to  refer  to, 
or  identify,  some  individual  object.  Proper  names  are 
all  singular.  It  is  true  that  proper  names  are  some- 
times used  to  denote  a  class  of  objects,  as,  e.g.,  'a. 
Daniel,'  '  a  Mephistopheles.'  But  when  thus  employed 
they  lose  their  real  character  as  proper  names.  That 
is,  their  function  is  no  longer  merely  to  identify  certain 
individuals  by  naming  them,  but  to  describe  them  by 
mentioning  certain  qualities  or  characteristics  which 
they  are  supposed  to  possess.  But  the  ordinary  pur- 
pose in  using  a  proper  name  is  to  indicate  some  indi- 
vidual to  whom  the  name  belongs.  In  this  sense,  then, 
proper  names  are  Singular. 

46 


§  12.   SINGULAR,  GENERAL,  AND  COLLECTIVE  TERMS       47 

In  addition,  any  word  or  group  of  words  which  is 
applied  to  a  single  thing  may  be  regarded  as  singular. 
And  by  'single  thing,'  we  mean  anything  which  is 
thought  of  as  one,  as  well  as  objects  which  are  per- 
ceived through  the  senses.  Thus,  'the  waterfall  just 
below  the  bridge,'  'the  centre  of  the  earth,'  are  singu- 
lar terms,  and  so  also  are  words  like  'justice,'  'good- 
ness,' 'the  chief  end  of  man.'  It  is  perhaps  more 
doubtful  whether  we  should  call  terms  such  as  'white- 
ness,' '  sweetness,'  singular,  since  we  speak  of  differ- 
ent degrees  and  kinds  of  whiteness  and  sweetness. 
The  question  would  have  to  be  decided  in  every  case 
by  reference  to  the  way  in  which  the  terms  are  em- 
ployed in  propositions. 

(2)  A  General   term  is  a  name  which  applies  to  a 
whole  group  of  objects.     It  is  not  limited,  like  the  sin- 
gular name,  to  a  single  thing,  but  applies  to  a  number 
of   different   things.      All   class    names    like    '  metal,' 
'man,'  'works  on  logic,'   are  of  this  character.     The 
general   name  belongs   to   each    and   every   individual 
of   a   whole   class.      Thus   iron,    gold,   silver,  etc.,  are 
'metals';    and  A,  B,  and  C,  'men.' 

(3)  A  Collective  term,  on  the  other  hand,  is  a  name 
applied  to  a  number  of  individuals  when  taken  together 
and  treated  as  a  whole,  as  'an  army,'  'an  audience.' 
It  is  important  to  distinguish  carefully  between  general 
and  collective  terms.     A  general  term  is  a  name  which 
applies  equally  to  each  individual  of  the  group ;  or,  in 
other  words,  it  is  used  of  the  individuals  distribntively. 
A  collective  name  belongs  to  the  whole,  but  not  to  the 
separate  parts  of  the  whole.     Thus  we  say  that  '  sol- 


48  THE  VARIOUS  KINDS  OF  TERMS 

dier '  is  a  general  name,  and  is  used  distributively  of 
each  man  in  a  regiment.  '  Regiment,'  however,  is  a 
collective  name,  for  it  applies  only  to  the  whole  group, 
and  not  to  the  individual  soldiers. 

Ambiguity  sometimes  arises  from  the  fact  that  the 
English  word  '  all '  is  used  in  both  of  these  senses. 
That  is,  it  may  mean  '  all  taken  together/  or  '  each  and 
every.'  Thus  we  can  say :  '  All  the  angles  of  a  tri- 
angle are  less  than  two  right  angles ' ;  and  '  all  the 
angles  of  a  triangle  are  equal  to  two  right  angles.'  In 
the  former  sentence,  the  word  '  all '  is  used  distribu- 
tively ;  in  the  latter,  collectively.  In  Latin  two  different 
words  are  used :  cuncti  expresses  the  collective  sense 
of  'all,'  and  omnes  its  distributive  signification. 

It  is  worth  noticing  in  this  connection  that  it  is  the  use  which 
is  made  of  terms,  rather  than  the  form  of  the  words  composing 
them,  which  determines  their  logical  character.  Thus  terms  which 
are  collective  in  one  connection  may  be  general  in  another.  '  Regi- 
ment,' for  example,  is  a  collective  term  with  reference  to  the  soldiers 
which  compose  it,  but  general  when  used  as  a  common  term  for  a 
number  of  similar  divisions  of  an  army.  The  same  is  also  true  of 
terms  like  ' grove,1  'mob/  'class/  etc.  Again,  collective  terms 
may  be  very  properly  regarded  as  singular  when  the  proposition 
in  which  they  are  used  emphasizes  the  unity  and  solidarity  of  the 
group.  A  proper  name  is  sometimes  applied  to  a  collection  of  in- 
dividuals that  are  permanently  united  or  that  have  acted  together 
on  some  historic  occasion,  as,  for  example,  '  The  Fifth  Cavalry  regi- 
ment/ '  The  Charge  of  the  Six  Hundred.1 

§  13.  Abstract  and  Concrete  Terms. — Terms  are  fur- 
ther divided  into  abstract  and  concrete  terms.  The 
word  *  abstract '  is  often  used  popularly  to  describe 
anything  which  is  difficult  to  understand.  Etymologi- 


§  is-     ABSTRACT  AND   CONCRETE  TERMS  49 

cally,  it  signifies  drawn  off,  separated  (abstraho,  to 
draw  off,  take  away).  We  may  distinguish  two  senses 
in  which  the  word  is  used,  both,  however,  being  derived 
from  its  etymological  signification. 

(i)  A  term  is  called  abstract  when  it  refers  to  some 
object  which  cannot  be  directly  perceived  through  the 
senses,  and  concrete  when  such  perception  is  possible. 
Thus  ' a  beech  tree,'  '  a  tall  man,'  'a  sweet  taste,'  being 
names  of  things  which  can  be  perceived,  are  concrete. 
Words  like  'sweetness,'  'hardness,'  etc.,  have  no  objects 
of  sense  directly  corresponding  to  them,  and  are  for 
this  reason  called  abstract.  The  same  is  true  of  terms 
like  'individuality,'  'equality,'  'justice/  etc.  These 
words  represent  objects  of  thought,  rather  than  ob- 
jects of  sense.  There  may  be  cases  or  instances  of 
'equality,'  'justice,'  etc.,  which  fall  under  our  percep- 
tion, but  the  real  object  to  which  these  words  corre- 
spond is  not  a  thing  which  can  be  perceived  through 
the  senses  at  all.  Their  reality  is  conceptual,  or  for 
thought,  not  something  directly  revealed  through  the 
senses. 

It  is  important  to  notice  that  there  are  degrees  of  abstractness  in 
terms,  according  as  the  objects  for  which  they  stand  are  nearer  to,  or 
further  removed  from  ordinary  sense-perception.  All  general  or 
class  names  are  abstract.  One  cannot  point  to  a  single  object,  to 
which  the  term  'metal,'  for  example,  or  the  term  *  man1  corresponds. 
But  although  such  terms  have  no  direct  sensuous  object,  yet  we  feel 
that  they  stand  nearer  to  sense-perception,  and  are  therefore  less 
abstract,  than  words  like  'animal,1  'inorganic  substance.1  These 
terms,  again,  are  perhaps  less  abstract  than  '  energy,1  or  <  spirit,1  or 
even  than  singular  terms  like  'justice,1  'the  ground  of  the  universe,7 
etc. 


5<D  THE  VARIOUS   KINDS   OF  TERMS 

(2)  Again,  the  word  '  abstract '  is  applied  to  any  ob- 
ject which  is  treated  apart  from  the  whole  to  which  it 
belongs.  Thus  it  would  be  an  abstraction  to  attempt 
to  represent  the  nature  of  a  leaf  in  complete  isolation 
from  the  plant  to  which  it  belongs,  or  to  consider  the 
nature  of  a  man  without  regard  to  the  social  institu- 
tions —  family,  church,  state,  etc.  —  of  which  he  is  a 
member.  Of  course,  it  is  essential  when  dealing  with  a 
complex  whole  to  analyze  it  into  its  parts,  and  to  under- 
stand just  what  is  the  nature  of  each  part  when  taken 
by  itself.  But  in  order  to  comprehend  fully  the  nature 
of  the  parts,  it  is  necessary  to  restore  them  to  their 
proper  setting,  and  to  see  their  relation  to  the  concrete 
whole.  In  this  sense  t)f  the  word,  then,  *  abstract' 
applies  to  what  is  taken  out  of  its  proper  setting,  broken 
off,  and  considered  apart  from  the  things  to  which  it  is 
organically  related.  Concrete,  on  the  other  hand,  means 
what  is  whole  and  complete,  a  system  of  things  which 
mutually  support  and  explain  one  another. 

Since  science  has  to  analyze  things  into  their  elements, 
and  to  investigate  and  describe  these  elements  in  detail, 
it  is  impossible  entirely  to  avoid  abstraction.  But  it  is 
necessary,  in  order  to  completely  understand  the  nature 
of  a  complex  object,  that  the  abstractions  of  analysis 
shall  be  corrected.  In  other  words,  the  concrete  rela- 
tions in  which  things  stand  must  not  be  ignored  in 
investigating  them.  The  conception  of  evolution  in 
recent  times  has  done  much  to  render  the  biological 
sciences  more  concrete  in  the  sense  in  which  we  are 
now  using  the  term.  For  it  has  substituted,  for  the  old 
method  of  treating  each  species  of  plant  and  animal  as 


§13.     ABSTRACT  AND   CONCRETE  TERMS  51 

distinct  and  separate,  '  cut  off  from  each  other  as  if  by 
a  hatchet,'  the  view  that  all  organic  beings  are  members 
of  one  family,  and  can  be  properly  understood  only  in 
their  relations  to  one  another. 

It  is  interesting  to  notice  that,  from  this  point  of  view,  sense- 
perception  is  more  abstract  than  thought.  For  the  senses  represent 
things  in  isolation  from  each  other.  Each  thing  is  known  in  sense- 
perception  as  a  separate  individual,  occupying  its  own  space  and 
time,  and  in  this  way,  cut  off  from  its  fellows.  It  is  the  business  of 
thought,  on  the  other  hand,  to  discover  the  relations  between  things, 
and  the  principles  according  to  which  they  are  united.  Thinking 
thus  overcomes  the  abstract  point  of  view  of  sense-perception  by 
showing  that  what  appear  to  the  latter  as  separate  objects  are 
really  closely  and  necessarily  connected  as  members  of  a  com- 
mon unity  or  system.  Each  science  takes  as  its  province  certain 
facts  which  resemble  one  another,  but  which  nevertheless  appear 
to  sense-perception  to  be  quite  independent.  It  attempts  by 
thinking  to  bring  these  facts  into  relation,  to  show  that  they  are 
all  cases  of  some  law,  that  there  is  a  common  principle  which  unites 
them  as  parts  of  a  whole  or  system.  The  law  of  gravitation,  for 
example,  expresses  the  unity  which  thought  has  discovered  in 
things  which  appear  to  sense-perception  as  different  as  the  falling 
of  an  apple,  the  movements  of  the  heavenly  bodies,  and  the  ebb 
and  flow  of  the  tides.  Scientific  knowledge,  then,  is  more  con- 
crete than  the  facts  which  we  learn  from  ordinary  sense-percep- 
tion, because  it  brings  to  light  real  unity  and  connection  in  facts 
which  appear,  to  be  entirely  isolated  and  independent  from  the 
latter  point  of  view. 

In  employing  the  terms  'Abstract'  and  'Concrete'  it 
is  of  the  utmost  importance  to  distinguish  the  two  sig- 
nifications of  the  words.  From  one  point  of  view,  as  we 
have  seen,  all  thought  terms  are  abstract,  as  opposed  to 
words  which  refer  directly  to  objects  of  sense-perception. 


52  THE  VARIOUS  KINDS   OF  TERMS 

In  another  sense,  '  abstract '  denotes  what  is  partial  and 
incomplete,  what  is  taken  by  itself  and  out  of  relation 
to  the  system  of  things  to  which  it  belongs.  And  since 
the  real  connection  and  relations  of  things  are  not  given 
by  perception,  but  have  to  be  discovered  by  thought, 
the  knowledge  which  the  latter  yields  is  more  concrete, 
in  this  latter  sense  of  the  term,  than  that  afforded  by 
the  former. 

§  14.  Positive  and  Negative  Terms. — The  distinction 
between  Positive  and  Negative  terms  is  very  obvious. 
Positive  terms  express  the  existence  of  some  quality,  or 
group  of  qualities,  in  the  objects  which  they  denote ;  as, 
e.g.,  'happy,'  'good,'  'equality,'  'organism,'  etc.  A  Neg- 
ative term,  on  the  other  hand,  indicates  the  absence 
of  qualities  or  properties  in  some  object ;  '  bad,'  '  un- 
happy,' 'inorganic,'  '  injustice,'  for  example,  are  negative 
terms.  Negative  terms  are  often  formed  from  positive 
by  means  of  the  affix,  less,  as  in  '  hopeless,'  or  by  means 
of  certain  prefixes,  of  which  the  more  common  are  un,  in, 
dis,  a,  anti.  Words  which  are  positive  in  form  are,  how- 
ever, often  negative  in  meaning,  and  are  used  as  the 
contradictories  of  other  terms.  Thus  'ignorant'  is 
generally  regarded  as  the  negative  of  '  learned,'  '  dark- 
ness '  is  the  negative  of  '-light,'  etc.  It  is  not  always 
possible,  however,  to  find  a  separate  word  to  express  the 
exact  opposite  of  every  positive  term.  Words  are  used 
primarily  to  express  the  presence  of  qualities,  and  the 
negative  idea  may  not  be  referred  to  so  frequently  as 
to  require  a  separate  word  to  express  it.  Thus  there 
is  no  independent  term  to  express  the  opposite  of  '  trans- 


§  I4.     POSITIVE  AND  NEGATIVE  TERMS  53 

ferable/  but*  by  employing  '  not '  as  a  negative  prefix  we 
obtain  'not-transferable.' 

It  is  always  advisable  when  we  wish  to  limit  a  term  strictly  to  its 
negative  application  to  employ  not  or  non  as  a  prefix.  Words 
which  are  negative  in  form  frequently  have  a  more  or  less  definite 
positive  signification.  Jevons  points  out  that  words  like  '  unloosed1 
and  '  invaluable,1  though  negative  in  form,  have  a  positive  meaning. 
But,  in  addition,  terms  like  '  unhappy,'  '  immoral,'  do  not  merely 
indicate  the  absence  of  positive  qualities,  but  also  express  some 
positive  properties  of  the  objects  to  which  they  are  applied.  We 
speak  of  a  person  '  being  positively  unhappy ' ;  and  we  employ 
'non-moral1  to  express  the  simple  negative  relation  rather  than 
'immoral.1 

On  the  other  hand,  there  are  certain  terms  which  are  positive  in 
form  that  express  the  absence  of  qualities  or  attributes.  Words  like 
'blind,1  'dumb,1  'maimed,'  'orphaned,1  may  be  given  as  examples. 
These  are  often  called  Privative  terms,  rather  than  Negative,  the 
distinction  being  that  they  refer  to  qualities  or  attributes  which  the 
objects  to  which  they  are  applied  naturally  and  usually  have,  but  of 
which  they  have  been  deprived,  or  which  they  have  never  possessed. 
Thus  '  blind,'  as  applied  to  a  man,  implies  that  he  has  lost  or  is  desti- 
tute of  the  ability  to  see  which  naturally  belongs  to  a  human  being. 

Again,  other  terms  seem  to  be  positive  and  negative  solely  in 
relation  to  each  other.  '  Element 1  and  '  compound '  are  related  as 
negatives  or  contradictories.  It  is  difficult,  however,  to  say  which 
term  is  in  itself  negative  or  positive. 

It  is  important  to  notice  the  distinction  between  the 
relation  in  which  positive  and  negative  terms  stand  to 
each  other,  and  that  expressed  by  words  which  have 
to  do  with  opposite  extremes  of  something  which  pos- 
sesses quality  or  degree.  Positive  and  negative  terms 
are  mutually  contradictory.  An  element  is  what  is  not 
a  compound,  '  dishonest '  is  the  contradictory  of  '  honest/ 


54  THE  VARIOUS  KINDS  OF  TERMS 

and  as  contradictories  there  is  no  middle  ground  be- 
tween them.  What  is  not  an  element,  is  a  non-element 
or  a  compound.  Opposite  or  contrary  terms,  on  the 
other  hand,  express  a  great  difference  of  degree  in  the 
objects  to  which  they  refer.  Thus  '  foolish '  is  the  op- 
posite of  '  wise,'  '  cold  '  the  opposite  of  '  hot,'  and  '  bitter ' 
of  '  sweet.'  But  there  is  always  the  possibility  of  a 
middle  ground  between  opposites.  We  cannot  say  that 
a  man  must  be  either  wise  or  foolish,  a  taste  either 
sweet  or  bitter.  The  logical  contradictory  of  '  wise '  is 
'not-wise,'  of  'bitter,'  is  'not-bitter,'  etc.  Opposite  or 
contrary  terms,  then,  must  be  carefully  distinguished 
from  contradictories. 

§  15.  Absolute  and  Relative  Terms. — Another  classi- 
fication of  terms,  which  is  usually  given  by  logicians, 
is  that  into  absolute  and  relative  terms.  An  absolute 
term  is  one  which  refers  to  an  object  which  exists  by 
itself,  and  has  an  intelligible  meaning  when  taken  alone. 
Thus,  'tree,'  'house,'  'the  State  of  New  York,'  are  ex 
amples  of  absolute  terms.  A  relative  term,  on  the  con- 
trary, is  a  name  which  only  derives  a  meaning  from  its 
relation  to  something  else.  The  term  'parent,'  for  ex- 
ample, cannot  be  thought  of  except  in  relation  to  'child.' 
Similarly,  'teacher'  is  relative  to  'pupil,'  and  'cause'  to 
'effect.'  Relative  terms  usually  go  in  pairs  and  are 
known  as  Correlatives.  Adjectives,  as  well  as  nouns, 
may  be  related  in  this  way.  The  presence  of  one 
quality  or  characteristic  in  a  thing  frequently  implies 
the  presence  of  others.  Thus,  ignorance  and  super- 
stition, sympathy  and  tolerance,  are  necessary  correla- 


§  i6.    EXTENSION  AND   INTENSION  OF  TERMS         55 

tives,  because  the  one  involves  the  other,  or  is  invariably 
connected  with  it. 

It  is  of  course  true  that  no  finite  thing  is  completely  absolute  or 
independent  of  other  things.  The  nature  of  everything  is  largely 
determined  by  the  nature  of  the  other  things  with  which  it  stands 
in  relation.  A  tree,  for  example,  is  relative  to  the  seed  from  which 
it  sprang,  the  soil  in  which  it  grew,  the  sunshine,  rain,  etc.,  which 
accompanied  its  growth.  All  finite  things  have  a  beginning  and  an 
end,  and  are  also  influenced  throughout  the  whole  period  of  their 
lives  by  the  action  of  other  things.  They  are  therefore  not  com- 
pletely absolute  or  independent.  It  is,  however,  possible  to  make  a 
distinction  between  words  which  are  the  names  of  things  that  are 
comparatively  independent,  and  may  for  ordinary  purposes  be  con- 
sidered by  themselves,  and  those  which  have  only  a  meaning  when 
regarded  as  correlatives. 

§   1 6.    Extension   and    Intension    of   Terms.  —  In    the 

foregoing  sections  of  this  chapter  we  have  explained 
the  nature  of  the  various  kinds  of  terms  with  which 
logic  deals.  It  is  now  necessary  to  notice  two  different 
purposes  for  which  terms  are  employed.  In  the  first 
place,  terms  are  used  to  refer  to  things,  to  name  and 
identify  them.  Thus  '  man '  refers  to  the  different 
individual  men,  John  Smith,  Thomas  Brown,  etc.,  as 
well  as  to  the  various  classes  of  men,  Caucasians, 
Indians,  Mongolians,  etc.  As  dendting  or  naming  ob- 
jects, whether  these  be  individual  things  or  classes  of 
things,  terms  are  said  to  be  employed  in  Extension. 
But  words  are  also  used  to  describe  as  well  as  to  name. 
That  is,  they  represent  the  qualities  or  attributes  be- 
longing to  things  for  which  they  stand.  They  are  not 
bare  names  without  signification,  but  as  the  expression 


56  THE   VARIOUS   KINDS  OF  TERMS 

of  ideas  they  stand  for  certain  qualities  or  character- 
istics which  things  are  judged  to  possess.  '  Man,'  for 
example,  is  not  merely  a  name  which  may  be  applied 
to  individual  human  beings  or  races  of  men,  but  it 
implies  that  the  objects  so  named  have  certain  qualities, 
such  as  animal  life,  reason,  and  the  power  of  com- 
municating with  their  fellows.  When  words  are  used 
in  this  way  to  define  or  describe  things,  rather  than 
merely  to  name  them,  they  are  said  to  be  employed  in 
Intension. 

The  terms  'Denotation'  and  'Connotation1  were  used  by  Mill 
instead  of  Extension  and  Intension,  respectively,  and  have  been 
adopted  pretty  generally  since  his  time.  To  'denote,'  is  to  point 
out  or  specify  the  objects  for  which  a  term  stands  ;  and  to  '  connote ' 
is  to  take  account  of  the  attributes  or  qualities  which  a  name  implies. 
The  words  '  breadth,'  and  '  comprehension,'  are  also  sometimes  used 
as  synonymous  with  Extension,  and  '  depth,'  or  '  content,1  instead  of 
Intension.  The  terms  to  be  remembered,  however,  are  Extension 
or  Denotation,  and  Intension  or  Connotation. 

It  is  useful  to  accustom  ourselves  to  distinguish  these 
two  functions  or  uses  of  a  term,  —  to  notice,  that  is,  the 
things  or  classes  of  things  to  which  the  name  applies,  — 
and  also  to  reflect  upon  the  signification,  or  ways  of  judg- 
ing about  these  things,  for  which  the  name  stands.  The 
Extension  of  a  term,  as  has  been  said,  indicates  the 
objects  to  which  a  name  applies,  and  the  Intension  the 
qualities  or  attributes  which  it  signifies.  From  the  point 
of  view  of  extension,  therefore,  *  planet '  may  be  defined 
by  mentioning  the  names  of  the  various  planets,  Mer- 
cury, Venus,  the  Earth,  Mars,  etc.  Similarly,  a  term 
like  '  carnivora '  might  be  given  in  extension  by  nam- 


§  1 6.     EXTENSION   AND   INTENSION   OF  TERMS          57 

ing  seals,  bears,  weasels,  dogs,  wolves,  cats,  lions,  etc. 
Usually,  however,  we  define  from  the  point  of  view  of 
intension,  that  is,  by  stating  the  qualities  or  character- 
istics for  which  the  term  stands.  Thus  we  give  the 
intensive  meaning  of  'planet,'  as  a  heavenly  body  which 
revolves  in  an  elliptical  orbit  round  the  sun.  '  Car- 
nivora,'  defined  from  the  same  point  of  view,  are  mam- 
malian vertebrates  which  feed  upon  flesh.  It  is  not 
unusual,  however,  to  supplement  an  intensive  definition 
by  turning  to  extension  and  enumerating  examples. 
Thus  we  might  add  to  the  definition  of  'carnivora'  just 
given,  the  words,  'as  lions,  tigers,  dogs,  etc.' 

It  is  sometimes  said  that  the  intension  and  extension 
of  terms  vary  inversely.  This  is  simply  an  attempt  to 
give  a  mathematical  form  of  statement  to  the  fact  that 
the  more  a  term  is  defined,  or  limited,  by  the  addition  of 
attributes,  the  fewer  are  the  objects  to  which  it  applies. 
'  As  the  intension  of  a  term  is  increased  its  extension  is 
diminished,  and  vice  versa,'  is  the  form  in  which  the 
relation  is  often  stated.  For  example,  let  us  begin 
with  some  class-name  like  '  animal,'  which  has  a  great 
extension,  and  add  a  new  attribute,  '  rational.'  We  get 
'  rational  animal '  =  man.  This  term  now  applies  to  a 
much  smaller  number  of  individuals  than  'animal.'  The 
extension  of  the  former  term  has  been  diminished,  that 
is,  by  increasing  the  intension.  If  we  add  to  'man'  still 
another  attribute  like  'white,'  we  again  lessen  the  num- 
ber of  individuals  to  which  the  term  applies.  In  gen- 
eral, then,  it  can  be  seen  that  the  extension  of  a  term 
is  lessened  as  it  is  made  more  definite  by  the  addition 
of  new  attributes.  And,  conversely,  by  stripping  off 


58  THE  VARIOUS  KINDS  OF  TERMS 

attributes,  by  'decreasing  the  intension,'  the  number 
of  individuals  to  which  a  term  applies  is  increased. 
There  is,  however,  no  exact  ratio  between  the  increase 
or  decrease  of  intension  and  the  corresponding  change 
in  extension.  Indeed,  the  extension  of  a  class  may 
increase  greatly  without  any  loss  of  intension  on  the 
part  of  the  term  by  which  the  idea  is  expressed.  Thus 
the  meaning  or  intension  of  the  term  '  man '  has  not 
lost  but  rather  gained,  during  the  last  hundred  years  by 
the  increase  of  population  throughout  the  world. 

Extension  and  intension,  according  to  the  view  just 
given,  represent  two  different  uses  or  functions  of  terms. 
Every  term  denotes  some  object  or  group  of  objects 
more  or  less  directly,  and  at  the  same  time  connotes  or 
signifies  certain  qualities  or  attributes.  Sometimes  the 
one  purpose,  sometimes  the  other,  is  the  predominant 
one.  Proper  names,  for  example,  are  used  primarily 
to  denote  or  mark  out  things,  and  do  not  directly 
qualify  or  describe  them.  In  the  proposition,  'these 
animals  are  all  vertebrates,'  the  predicate  term  '  verte- 
brates '  is  employed  less  as  a  name  of  a  number  of 
animals,  than  as  a  description  of  their  qualities.  Never- 
theless, in  both  these  cases  the  terms  employed  have  the 
double  function  of  naming  or  denoting  objects,  and  of 
connoting  qualities. 

Mill,  however,  and  certain  other  logicians  who  follow 
him,  make  a  distinction  between  connotative  and  non- 
connotative  terms.  "A  non-connotative  term  is  one 
which  signifies  a  subject  only,  or  an  attribute  only.  A 
connotative  term  is  one  which  denotes  a  subject,  and 
implies  an  attribute.  By  a  subject  is  here  meant  any- 


§  16.     EXTENSION   AND    INTENSION   OF  TERMS          59 

thing  which  possesses  attributes.  Thus  '  John,'  or  '  Lon- 
don,' or  '  England '  are  names  which  signify  a  subject 
only.  '  Whiteness,'  '  length,'  'virtue,'  signify  an  attribute 
only.  None  of  these  names,  therefore,  are  connotative. 
But  'white,'  'long,'  'virtuous,'  are  connotative.  The 
word  '  white '  connotes  all  white  things,  as  snow,  paper, 
the  foam  of  the  sea,  etc.,  and  implies  or,  as  it  was  termed 
by  the  schoolmen,  connotes  the  attribute  whiteness.  .  .  . 
All  concrete  general  names  are  connotative.  The  word 
'man,'  for  example,  denotes  Peter,  James,  John,  and  an 
indefinite  number  of  other  individuals,  of  whom,  taken 
as  a  class,  it  is  the  name.  But  it  is  applied  to  them 
because  they  possess,  and  to  signify  that  they  possess, 
certain  attributes."1 

There  is  no  real  ground,  I  think,  for  such  an  abso- 
lute distinction  between  connotative  and  non-connota- 
tive  terms.  When  we  consider  the  use  or  function  of 
terms,  we  find  that  they  are  never  used  merely  to  name 
things,  or  merely  to  connote  attributes,  though  in  cer- 
tain cases  the  former  purpose  is  the  primary  one,  and 
in  other  cases  the  latter  object  is  more  prominent. 
Even  when  proper  names  are  employed,  the  qualities  or 
characteristics  of  the  objects  named  are  indirectly  im- 
plied. The  very  fact  that  a  proper  name  is  given  to 
an  object  implies  that  it  possesses  a  certain  definitely 
marked  individuality.  And  a  proper  name  when  used 
intelligently  carries  with  it  some  still  more  definite  im- 
formation  regarding  the  qualities  of  the  thing  to  which 
it  is  applied,  as,  for  example,  whether  it  is  a  name  of  a 
person,  an  animal,  or  a  place. 

1  Mill,  System  of  Logic,  Bk.  I.  Ch.  II.  §  5. 


60  THE  VARIOUS   KINDS   OF  TERMS 

The    reader    may   consult,   in    connection   with   this 
chapter :  — 

J.  S.  Mill,  Logic,  Bk.  I.  Ch.  II. 

F.  H.  Bradley,  The  Principles  of  Logic,  pp.  155-173. 

B.  Bosanquet,  Logic,  Vol.  I.,  pp.  46-71. 

"  "          The  Essentials  of  Logic,  Lecture  V. 


CHAPTER   V 

DEFINITION    AND    DIVISION 

§  17.  Fixing  the  Meaning  of  Terms.  --We  have  al- 
ready referred  to  the  necessity  of  definitely  fixing  the 
meaning  of  the  terms  which  we  employ  in  reasoning. 
In  ordinary  life,  words  are  frequently  used  in  a  loose 
and  shifting  way,  without  any  clear  conception  of  the 
qualities  or  properties  which  they  connote,  or  of  the 
objects  to  which  they  apply.  Logic  demands,  in 
the  first  place,  that  we  shall  have  clear  and  definite 
ideas  corresponding  to  our  words,  and  that  the  signifi- 
cation and  scope  of  the  latter  shall  be  carefully  deter- 
mined. But  this  is  a  demand  to  which  little  attention 
is  paid  in  the  ordinary  affairs  of  life.  To  define  our 
terms  in  explicit  language,  or  even  to  make  clear  to 
ourselves  the  ideas  and  things  for  which  they  stand,  is 
by  no  means  a  natural  or  a  universal  mode  of  proced- 
ure, but  something  which  requires  a  distinct,  conscious 
effort. 

Bacon,  Hobbes,  Locke,  Hume,  and  nearly  all  of  the 
older  philosophical  writers  have  warned  us  against  the 
abuse  of  words.  The  whole  matter  has  been  expressed 
very  clearly  by  Locke,  from  whom  I  quote  the  follow- 
ing passage :  — 

"  For  he  that  should  well  consider  the  errors  and 
obscurity,  the  mistakes  and  confusion,  that  are  spread 

61 


62  DEFINITION   AND    DIVISION 

in  the  world  by  an  ill  use  of  words  will  find  some 
reason  to  doubt  whether  language,  as  it  has  been 
employed,  has  contributed  more  to  the  improvement 
or  hindrance  of  knowledge  amongst  mankind.  How 
many  are  there,  that  when  they  would  think  on  things 
fix  their  thoughts  only  on  words,  especially  when  they 
would  apply  their  minds  to  moral  matters ;  and  who 
then  can  wonder  if  the  result  of  such  contemplations 
and  reasonings,  whilst  the  ideas  they  annex  to  them 
are  very  confused  and  very  unsteady,  or  perhaps  none 
at  all ;  who  can  wonder,  I  say,  that  such  thoughts  and 
reasonings  end  in  nothing  but  obscurity  and  mistake, 
without  any  clear  judgment  or  knowledge  ? 

"  This  inconvenience  in  an  ill  use  of  words  men  suffer 
in  their  own  private  meditations ;  but  much  more 
manifest  are  the  discords  which  follow  from  it  in  con- 
versation, discourse,  and  arguments  with  others.  For 
language  being  the  great  conduit  whereby  men  convey 
their  discoveries,  reasonings,  and  knowledge  from  one 
to  another;  he  that  makes  an  ill  use  of  it,  though  he 
does  not  corrupt  the  fountains  of  knowledge  which  are 
in  things  themselves ;  yet  he  does,  as  much  as  in  him 
lies,  break  or  stop  the  pipes  whereby  it  is  distributed  to 
the  public  use  and  advantage  of  mankind."  1 

The  remedy  for  the  obscurities  and  confusions  of 
words  is  to  be  found  in  clear  and  distinct  ideas.  We 
must  endeavour  to  go  behind  the  words  and  realize 
clearly  and  distinctly  in  consciousness  the  ideas  for 
which  they  stand.  Now  the  means  which  logic  re- 

1  Essay  concerning  Human  Understanding,  Bk.  III.  Ch.  XI. 


§  1 8.     DEFINITION  63 

commends  for  the  attainment  of  this  end  is  definition. 
The  first  requirement  of  logical  reasoning  is  that  terms 
shall  be  accurately  defined.  There  are,  however,  two 
ways  in  which  the  meaning  of  a  term  may  be  defined 
or  explained.  Every  term,  as  we  have  already  seen 
(§  16),  may  be  regarded  either  from  the  point  of  view 
of  intension,  or  from  that  of  extension.  To  define  in 
the  narrower  sense  is  to  explain  from  the  standpoint 
of  intension,  to  state  the  attributes  or  qualities  which 
are  connoted  by  the  term.  The  process  of  explaining 
terms  with  reference  to  the  objects,  or  classes  of  objects, 
for  which  they  stand  is  known  as  Division.  We  may 
include,  then,  under  the  general  term  definition,  (i)  In- 
tensive definition,  or  definition  in  the  narrower  sense, 
and  (2)  Extensive  definition  or  division. 

§  1 8.  Definition.  — To  define  a  term  is  to  state  its 
connotation,  or  to  enumerate  the  attributes  which  it 
implies.  Thus  we  define  a  parallelogram  as  a  quadri- 
lateral figure  whose  opposite  sides  are  parallel.  A 
distinction  is  often  made  between  verbal  and  real  defi- 
nition. When  we  merely  wish  to  explain  the  mean- 
ing in  which  we  intend  to  employ  some  term,  we  have 
verbal  definition.  But  when  it  is  the  purpose  of  our 
assertion  to  state  the  real  nature  or  essential  character- 
istics of  some  object,  the  proposition  employed  is  said 
to  constitute  a  real  definition.  This  distinction,  though 
not  without  importance,  cannot,  I  think,  be  regarded  as 
ultimate.  For  we  never  define  a  word  or  term  for  its 
own  sake  merely,  but  in  order  to  understand  the  nature 
of  the  objects  to  which  it  refers.  Indeed,  a  mere  word, 


64  DEFINITION  AND   DIVISION 

apart  from  the  things  for  which  it  stands,  has  no  inter- 
est for  us.  In  defining  a  term,  then,  we  are  always 
attempting  to  explicate  or  explain,  more  or  less  directly, 
the  nature  of  a  thing,  or  our  idea  about  a  thing. 

Nevertheless,  there  is  an  advantage  in  distinguishing 
propositions  whose  immediate  purpose  is  to  expound 
the  meaning  of  a  word,  from  those  which  assert  some- 
thing directly  of  an  object.  *  Monarchy  consists  in  the 
authority  of  one  man  over  others,'  may  be  regarded  as 
a  verbal  definition,  because  the  purpose  of  the  propo- 
sition is  simply  to  explain  the  meaning  of  the  subject 
term.  On  the  other  hand,  '  iron  is  malleable '  is  a  real 
definition  (though  not  a  complete  one),  because  it  does 
not  primarily  refer  to  the  signification  of  the  word 
4  iron,'  but  to  the  real  object  to  which  the  name  is  ap- 
plied. 

In  this  connection,  it  is  interesting  to  notice  that  a  proposition 
which  amounts  to  nothing  more  then  a  verbal  definition,  is  some- 
times put  forward  as  if  it  were  an  assertion  which  contained  some 
real  knowledge.  The  solemn  commonplaces  in  which  ignorant  per- 
sons delight  are  often  of  this  character.  '  A  republic  is  a  govern- 
ment by  the  people,'  '  a  just  man  will  do  what  is  right,'  *  if  it  rains, 
the  ground  will  be  wet,'  may  serve  as  examples.  The  mistake  in 
such  cases  consists  in  supposing  that  these  assertions  are  anything 
more  than  verbal. 

There  are  two  points  of  view  from  which  the  subject 
of  definition  may  be  considered.  We  might  either 
discuss  the  best  method  of  obtaining  real  definitions  of 
the  nature  of  things,  or  might  confine  our  attention  to 
the  requirements  which  a  good  definition  has  to  fulfil. 
A  person's  ability  to  define  either  a  term,  or  the  thing 


§  1 8.     DEFINITION  65 

for  which  the  term  stands,  depends,  however,  upon  the 
possession  of  clear  and  distinct  ideas  on  the  subject. 
The  problem,  then,  as  to  the  best  method  of  finding 
definitions,  resolves  itself  into  an  inquiry  concerning 
the  means  to  be  used  in  obtaining  and  classifying  our 
ideas  in  general ;  and  the  answer  to  this  question,  so 
far  as  an  answer  can  be  given,  must  be  found  in  the 
theory  of  logic  as  a  whole.  In  our  treatment  of  the 
subject  we  shall,  therefore,  confine  our  attention  mainly 
to  a  consideration  of  the  requirements  of  a  logical 
definition,  and  the  rules  which  must  be  observed  in 
stating  it  in  language. 

Before  entering  upon  the  subject,  however,  it  is  in- 
teresting to  refer  briefly  to  the  method  proposed  by 
Socrates  for  obtaining  definitions.  Socrates,  as  we 
have  already  seen  (§  5),  was  the  first  to  emphasize 
the  necessity  of  defining  and  fixing  the  meaning  of 
familiar  terms.  He  found  that,  though  the  people  of 
Athens  were  constantly  using  terms  like  'good,'  'beau- 
tiful,' 'justice,'  and  'temperance,'  none  of  them,  not 
even  those  with  the  greatest  reputation  for  wisdom,  were 
able  to  give  any  clear  and  consistent  statement  of  what 
these  terms  implied.  Socrates  himself  did  not  profess 
to  be  wiser  than  the  rest,  but  he  had  a  genuine  spirit 
of  inquiry,  and  made  it  the  business  of  his  life  to  try  to 
arrive  at  clear  conceptions,  especially  with  regard  to 
certain  fundamental  ethical  virtues,  like  justice,  and 
temperance,  and  wisdom,  which  he  regarded  as  of  the 
utmost  practical  importance.  It  was  by  means  of  con- 
versation with  others  that  he  sought  to  gain  clear 
ideas  regarding  the  nature  of  these  virtues.  By  a 

F 


66  DEFINITION  AND   DIVISION 

series  of  questions  and  answers,  by  comparison  of 
any  definition  proposed  with  particular  facts  which  are 
admitted,  he  led  his  interlocutors  to  expose  and  refute 
the  inadequacies  of  their  earlier  statements.  In  the 
Republic,  for  example,  the  question  is  regarding  the 
nature  of  justice.  The  first  definition  suggested  is, 
that  it  is  just  'to  speak  the  truth,  and  to  restore  to 
each  man  his  own.'  But  supposing  that  a  man  were 
out  of  his  mind  and  demanded  his  weapons  which  had 
been  placed  in  the  hands  of  a  friend,  would  the  friend 
be  an  unjust  man  if  he  refused  to  return  the  weapons, 
or  abstained  from  telling  the  whole  truth  ?  Evidently 
not.  The  definition  is  then  modified  to  read,  '  It  is  just 
to  give  to  each  man  what  is  his  due.'  Socrates  then 
questions  further,  What  is  due  to  each  man  ?  What  is 
due  to  a  friend,  and  what  to  an  enemy  ?  This  leads  to 
the  further  modification  that  'justice  means  doing  good 
to  our  friends  and  harm  to  our  enemies.'  By  referring 
again  to  particular  instances  and  familiar  analogies, 
Socrates  leads  the  person  maintaining  this  definition 
to  admit  that  to  injure  a  person  is  to  make  him  less 
virtuous,  and  therefore  less  just.  But  how  can  justice 
render  the  character  of  another  less  just  than  it  was 
before  ?  The  idea  is  absurd ;  therefore  the  definition 
has  to  be  abandoned,  and  a  fresh  start  made. 

This  method  of  proceeding  by  means  of  question  and 
answer,  and  thus  compelling  a  speaker  to  admit  par- 
ticular facts  which  refute  the  general  thesis  which  he 
is  maintaining,  is  called  Dialectic.  This  was  the  means 
by  which  Socrates  constantly  strove  to  advance  to  consis- 
tent and  adequate  definitions.  Apart  from  the  dialectical 


§  1 8.     DEFINITION  67 

and  dramatic  form  which  the  Socratic  argument  took, 
the  method  employed  is  essentially  that  of  induction. 
For  the  definition,  or  conception,  is  derived  from  a  com- 
parison of  particular  instances,  both  positive  and  nega- 
tive. By  a  consideration  of  individual  cases,  Socrates 
sought  to  obtain  a  definition  which  would  be  a  complete 
and  adequate  expression  of  the  nature  of  all  the  individ- 
uals which  share  in  the  class  name.  Aristotle  says  that 
it  is  to  Socrates  we  owe  the  method  of  induction  and 
logical  definitions.  Clear  and  distinct  conceptions,  for- 
mulated in  exact  definitions,  constituted  the  scientific 
goal  for  Socrates,  and  the  inductive  procedure  of  ob- 
serving and  classifying  particular  instances  was  the 
means  which  he  employed  for  reaching  this  goal. 

The  second  question  has  reference  to  the  formulation 
of  a  definition  in  language.  Suppose  that  we  already 
possess  a  clear  conception  of  the  meaning  of  the  terms 
to  be  defined,  what  are  the  conditions  which  a  logical 
definition  must  fulfil  ?  The  answer  to  this  question  is 
usually  given  in  logical  text-books  by  means  of  a  set 
of  rules  for  definition.  Before  stating  these  rules,  how- 
ever, it  is  necessary  to  explain  the  meaning  of  the  terms 
1  genus,'  'species,'  and  'differentia,'  which  will  be  fre- 
quently employed  throughout  the  remainder  of  this 
chapter.  These  terms,  together  with  '  property '  and 
'accident,'  constitute  what  the  older  logicians  call  the 
predicables,  and  to  which  a  great  deal  of  importance 
was  supposed  to  belong.  It  will  only  be  necessary, 
however,  for  us  to  consider  briefly  the  signification  of 
the  first  three  terms. 


68  DEFINITION   AND   DIVISION 

In  logic,  any  term  may  be  regarded  as  a  genus  which 
contains  two  or  more  subordinate  classes  or  species. 
A  species,  on  the  other  hand,  is  simply  a  subdivision  or 
subordinate  class  of 'some  larger  whole.  Thus  'metal' 
is  a  genus  with  reference  to  iron,  gold,  silver,  etc., 
which  are  its  species.  '  Rectilinear  figure '  is  the  genus 
to  which  belong  the  various  species,  triangle,  quadri- 
lateral, pentagon,  etc.  The  differentia  of  any  term  is 
made  up  of  the  qualities  or  characteristics  which  dis- 
tinguish it  from  other  terms,  from  the  genus  to  which 
it  belongs,  as  well  as  from  the  species  which  are  co- 
ordinate with  it.  Thus  the  logical  differentia  of  a 
triangle,  is  the  property  of  having  three  sides,  the  dif- 
ferentia of  man,  is  that  which  distinguishes  him  from 
other  animals,  whether  this  be  the  power  of  speech  and 
reason,  or  some  other  characteristic  either  physical  or 
mental. 

The  use  of  the  terms  'genus'  and  'species'  in  logic  is 
entirely  relative.  That  is,  any  term  may  be  considered 
either  as  a  species  or  a  genus,  according  as  it  is  regarded 
as  forming  a  part  of  some  more  comprehensive  class,  or 
as  itself  including  other  classes.  Thus  man,  for  example, 
is  a  species  of  the  genus  '  animal ' ;  but  the  same  term 
also  may  be  regarded  as  a  genus  including  various  species 
of  men,  Caucasians,  Negroes,  Mongolians,  etc.  In  the 
same  way,  '  animal '  may  be  considered  a  species  of  the 
still  more  comprehensive  class  '  organized  being,'  and 
this  latter  term  again  as  a  species  of  the  genus  '  material 
being.'  A  still  higher  or  more  comprehensive  term 
which  includes  as  its  species  material  and  spiritual 
beings  alike  is  'being.'  Since  this  term  includes  every- 


§i8.     DEFINITION  69 

thing  which  exists,  and  can  therefore  never  be  included 
in  any  more  'general  class,  it  is  sometimes  called  the 
highest  genus  '  (summum  genus}.  On  the  other  hand, 
we  might  proceed  downwards  until  we  come  to  a  class 
which  did  not  admit  of  division  into  any  subordinate 
classes.  Such  a  term  is  called  in  logic  the  lowest 
species  (infima  species). 

It  is  important  to  notice  that  the  terms  '  genus '  and  '  species '  have 
not  the  same  signification  in  logic  as  in  the  natural  sciences.  In 
classifying  objects  in  natural  history,  we  use  the  terms  <  variety,' 
*  species,  *  genus,1  'family,'  and  'order,'  to  denote  varying  degrees  of 
relationship  between  certain  groups  or  classes  of  objects.  These 
terms,  as  thus  employed,  also  indicate  certain  relatively  fixed  divi- 
sions, or  permanent  ways  of  grouping  the  various  forms  of  plant  and 
animal  life.  But  in  logic  the  terms  '  genus '  and  *  species '  are  em- 
ployed to  indicate  the  relationship  between  any  higher  and  lower 
class  whatsoever.  Moreover,  as  we  have  seen,  any  term  (excepting 
only  the  highest  genus  and  the  lowest  species)  may  be  regarded 
from  different  standpoints,  as  either  a  genus  or  a  species. 

We  shall  now  proceed  to  state  the  requirements  of  a 
logical  definition :  — 

(i)  A  definition  should  state  the  essential  attributes 
of  the  thing  to  be  defined.  This  is  done  by  stating  the 
genus  to  which  the  object  belongs,  and  also  the  pecul- 
iar marks  or  qualities  by  means  of  which  it  is  distin- 
guished from  other  members  of  the  same  class.  Or 
as  the  rule  is  usually  stated :  A  logical  definition 
should  give  the  next  or  proximate  genus,  and  the  dif- 
ferentia of  the  species  to  be  defined.  Thus  we  define 
a  triangle  as  a  rectilinear  figure  (genus),  having  three 
sides  (differentia) ;  and  man  as  an  animal  (genus),  which 
has  the  power  of  speech  and  reason  (differentia). 


70  DEFINITION  AND   DIVISION 

(2)  A   definition  should  not  contain  the   name   to   be 
defined,  nor  any  word  which  is  directly  synonymous  with 
it.     If,  for  example,  we  were  to  define  justice  as  the 
way  of  acting  justly,  or  life  as  the  sum  of  vital  pro- 
cesses, we  should  be  guilty  of  a  violation  of  this  rule. 

(3)  The  definition  should  be  exactly  equivalent  to  the 
class  of  objects  defined,  that  is,  it  must  be  neither  too 
broad  nor  too  narrow.     In  other  words,  the  definition 
must  take  account  of  the  whole  class  and  nothing  but 
the  class.     '  A  sensation  is  an  elementary  state  of  con- 
sciousness/ for  example,  is  too  broad  a  definition,  since 
it  applies  equally  to  affective  and  conative  elementary 
processes.     On  the  other  hand,  the  definition  of  gov- 
ernment as  'an  institution  created  by  the  people  for 
the  protection  of  their  lives  and  liberties,'  is  too  nar- 
row.    For  it  takes  no  account  of  absolute   forms   of 
government  which  do  not  depend  upon  the  will  of  the 
people.     Both    of   these   cases  may  be  regarded  as  a 
failure  to  give  the  true  differentia  of  the  class  to   be 
defined,  and  hence  as  violations  of  the  first  rule. 

(4)  A   definition  jhould  not  be  expressed  in  obscure, 
figurative,  or  ambiguous  language.     The  reasons   for 
this  rule  are  at  once  evident.     Any  lack  of  clearness 
or  definiteness  in  a  definition  renders  it  useless  as  an 
explanation.     Sometimes   the  words   used   in    defining 
may  be  less  familiar  than  the  term  to   be   explained 
(ignotum  per  ignotius).     The  definition  which  was  once 
given  of  the  word  '  net '  as  '  a  reticulated  texture  with 
large  interstices  or  meshes,'  may  serve  as  an  example. 

(5)  A  definition  should,  whenever  possible,  be  affirma- 
tive rather  than  negative.     A  definition,  that  is,  should 


§19.     DIVISION  ;i 

state  what  a  term  implies  rather  than  what  it  does  not 
imply.  Sometimes,  however,  the  purpose  of  a  defini- 
tion may  be  best  attained  by  a  negative  statement  of 
what  is  excluded  by  the  meaning  of  the  term.  Thus, 
for  example,  we  may  define  a  spiritual  being  as  a  being 
which  is  not  material,  that  is,  unlike  a  material  body 
made  up  of  parts  extended  in  space. 

A  logical  definition,  as  has  been  said,  requires  us  to  mention  the 
proximate  genus  or  next  higher  class  to  which  the  species  to  be  defined 
belongs,  and  also  the  specific  or  characteristic  differences  which  dis- 
tinguish it  from  other  species.  Now  it  is  clear  that  there  are  certain 
cases  in  which  these  conditions  cannot  be  fulfilled.  In  the  first 
place,  no  logical  definition  can  be  given  of  the  highest  genus,  be- 
cause there  is  no  more  general  class  to  which  it  can  be  referred. 
And  again,  although  it  is  possible  to  give  the  differentia  of  any 
species  such  as  '  man '  or  *  metal,'  it  is  not  possible  to  state  indi- 
vidual characteristics  by  means  of  a  logical  definition.  An  indi- 
vidual thing  may  be  perceived,  and  its  various  properties  pointed 
out.  But  it  is  never  possible  to  state  in  a  logical  definition  wherein 
the  individuality  of  a  particular  thing  consists.  The  uniqueness  of 
a  particular  object  cannot  be  summed  up  in  a  general  definition,  but 
must  be  learned  through  perception.  We  may  perhaps  say  that  the 
highest  genus  is  above,  and  the  individual  thing  below,  the  sphere  of 
logical  definition. 

There  are,  moreover,  other  terms  such  as  *  space,'  t  time,1  *  life,' 
*  thought,'  which  are  not  readily  referred  to  any  higher  class,  and 
for  which  therefore  logical  definitions  cannot  be  given.  These 
terms  are  sometimes  said  to  denote  objects  which  are  sui  generis, 
or  of  their  own  class. 

§  19.  Division. — We  have  already  spoken  of  divi- 
sion as  a  process  of  defining  a  term  from  the  point  of 
view  of  extension.  This  is  to  enumerate  the  objects 
or  classes  of  objects  which  the  term  denotes.  This 


72  DEFINITION   AND    DIVISION 

enumeration  must,  however,  be  guided  by  certain  prin 
ciples  which  we  have  now  to  consider. 

It  is  usual  to  begin  this  subject  by  speaking  of  Di- 
chotomy, or  the  division  of  a  term  into  two  parts  (St%a 
Te'fjiveiv,  to  cut  in  two).  This  is  a  purely  formal  process, 
and  is  based  on  the  so-called  law  of  Excluded  Middle, 
which  is  regarded  as  one  of  the  fundamental  laws  of 
thought.  This  law  may  be  stated  as  follows:  There 
is  no  middle  ground  between  contradictories.  Any  term, 
a,  is  either  b  or  not-£.  A  triangle  is  either  equilateral  or 
not-equilateral.  Of  two  contradictory  predicates,  one  or 
the  other  must  belong  to  every  possible  subject. 

Now  it  is  clear  that  this  is  a  purely  formal  principle 
of  division.  Some  positive  knowledge  of  the  particular 
facts  involved  is  always  necessary,  in  order  to  enable 
one  to  determine  what  things  do  stand  in  this  relation 
of  logical  opposition.  The  logical  law,  in  other  words, 
does  not  help  us  at  all  in  deciding  what  may  be  re- 
garded as  not-tf  in  any  particular  case.  It  is  not,  there- 
fore, a  means  of  increasing  our  knowledge,  but  merely 
a  principle  of  order  and  arrangement.  This  fact,  obvi- 
ous as  it  seems,  was  not  understood  by  the  Schoolmen 
who  busied  themselves  with  logic  in  the  latter  part  of 
the  Middle  Ages.  They  clung  firmly  to  the  belief  that 
it  was  possible  to  discover  the  nature  of  particular  facts 
by  purely  formal  operations  of  this  kind.  Accordingly, 
they  spent  a  great  deal  of  time  in  classifying  and  arrang- 
ing terms  as  contradictions,  contraries,  etc.  This  work 
was  doubtless  of  much  service  in  fixing  the  meaning  of 
terms,  and  in  preventing  confusion  in  their  employment. 
But  it  was  a  purely  verbal  investigation,  and  of  course 


§  19-     DIVISION  73 

could  not  lead  to  any  discoveries  regarding  the  nature 
of  things. 

Moreover,  it  must  be  noticed  that  we  do  not  always 
get  propositions  to  which  any  meaning  can  be  attached 
by  uniting  subjects  and  predicates  in  this  way.  If  the 
law  of  Dichotomy  is  not  guided  by  knowledge  of  the 
particular  facts,  it  will  give  absurd  propositions  like, 
'virtue  is  either  square  or  not-square,'  'iron  is  either 
pious  or  not-pious.'  Unmeaning  propositions  of  this 
kind  being  left  out  of  account,  however,  we  may  proceed 
to  divide  everything  according  to  this  principle.  All 
geometrical  figures  are  either  rectilinear  or  not-rec- 
tilinear; all  rectilinear  figures  either  triangular  or  not- 
triangular  ;  all  triangles,  equilateral  or  not-equilateral,  etc. 
This  method  of  division  may  be  represented  thus  :  — 

Substance 

I 


Material  non-material 


I  I 

Organic  not-organic 


mineral  not-mineral 

i 


I  I 

gold  not-gold 

If  it  were  desirable,  the  terms  'non-material,'  'organic,' 
and  'not-mineral'  might  also  be  further  subdivided  in 
the  same  way. 

Now  it  is  not  difficult  to  see  that  the  practical  use  of 
this  principle  will  depend  upon  our  ability  to  find  some 
positive  value  for  the  negative  not-a.  That  is,  to  make 
the  law  of  more  than  formal  value,  we  must  know  what 


74  DEFINITION  AND  DIVISION 

concrete  term  excludes  a,  or  is  its  logical  contradictory. 
And  knowledge  of  this  kind  comes,  as  already  said,  only 
from  experience  of  the  particular  facts.  The  strictly 
logical  contradictory  of  a  is  always  not-# ;  of  wise,  not- 
wise,  of  cold,  not-cold,  etc.  Mistakes  frequently  arise  in 
stating  contradictories  in  a  positive  form.  The  difficulty 
is  that  terms  are  chosen  which  are  not  true  logical  con- 
tradictories. Thus,  if  we  say  that  every  man  is  either 
wise  or  foolish,  our  terms  are  not  contradictory,  for  a 
middle  ground  between  them  is  possible.  The  same 
would  be  true  of  divisions  like,  'large  or  small/  'rich  or 
poor,'  'saint  or  sinner,'  'idle  or  diligent.'  In  general, 
it  is  safe  to  scrutinize  all  dichotomic  divisions  very 
sharply  to  see  that  the  alternatives  are  really  contra- 
dictories. 

The  method  of  dichotomy  depends,  as  we  have  seen, 
upon  the  law  of  Excluded  Middle.  But  there  is  also 
another  process  called  Division  in  logic,  which  is  per- 
haps better  known  by  its  less  technical  name  of  Classi- 
fication. In  classification,  there  is  no  necessary  limit 
to  the  number  of  classes  or  divisions  which  may  be  ob- 
tained. In  this  respect,  it  of  course  differs  fundamentally 
from  the  twofold  division  which  we  have  been  exam- 
ining. Furthermore,  a  classification  is  always  made 
according  to  some  principle  which  is  retained  through- 
out the  whole  process.  Any  common  characteristic  of 
the  group  of  individuals  to  be  divided  may  be  taken  as  a 
principle  of  classification.  If,  however,  the  characteristic 
chosen  is  merely  an  external  and  accidental  one,  the 
classification  based  upon  it  will  be  regarded  as  artificial, 
and  made  for  some  special  or  temporary  purposes, 


§  i9.     DIVISION  75 

Thus  we  might  divide  all  flowering  plants  according  to 
the  color  of  the  flowers,  or  the  persons  in  any  company 
according  to  the  pattern  of  their  shoes.  A  classification 
which  proceeds  upon  such  surface  distinctions  has,  of 
course,  no  real  or  scientific  value.  It  does  not  attempt 
to  discover  fundamental  or  deep-lying  resemblances  be- 
tween the  individuals  with  which  it  deals. 

A  scientific  or  natural  classification,  on  the  other  hand, 
has  for  its  purpose  the  discovery  of  real  likeness  or  resem- 
blance. It  seeks  to  find  and  group  together  the  things 
which  are  related  in  some  essential  point.  Consequently, 
it  selects  as  its  principle  of  division  some  property  which 
appears  to  be  a  real  mark  of  individuality,  and  to  be 
connected  with  changes  in  other  properties.  Such  a 
real  principle  of  natural  classification  is  rarely  found 
by  comparison  of  merely  one  property  or  set  of  prop- 
erties in  the  things  to  be  compared.  To  classify  accord- 
ing to  a  single  property  may  be  a  convenient  method 
of  giving  names  to  any  group  of  individuals,  and  of 
arranging  them  in  such  a  way  as  to  be  useful  to  the 
student.  It  does  not,  however,  give  any  adequate  idea 
of  the  properties  and  true  relations  of  the  individuals 
compared.  A  really  scientific,  or  natural,  classification 
must  be  based  upon  a  study  and  comparison  of  all 
the  discoverable  properties  of  the  different  individuals 
to  be  classified.  It  is  only  in  this  way  that  their  real 
resemblance  and  affinities  can  be  brought  to  light. 

(i)  The  classification  of  plants  proposed  by  the  famous  Swedish 
botanist,  Karl  Linnaeus  (1707-1778),  was  based  upon  the  comparison 
of  a  single  feature  :  the  structure  of  the  sexual  organs  of  plants.  This 
method  proved  of  the  greatest  convenience  in  indexing  plants  in  a 


76  DEFINITION  AND   DIVISION 

convenient  way  into  genera  and  species  so  that  they  could  be  named 
and  described.  Yet  since  the  classification  adopted  was  based  upon 
a  single  property  or  feature  of  the  plant,  it  was  considered  (even  by 
Linnaeus  himself)  as  merely  artificial.  Of  course  it  is  not  so  obvi- 
ously artificial  as  the  examples  of  what  we  may  perhaps  call  merely 
accidental  or  trivial  classification  given  above.  But  Linnaeus's 
system  did  not  aim  at  setting  forth  the  true  relations  of  plants,  and  it 
was  not  based  upon  any  systematic  study  of  all  their  properties.  It 
is  useful  merely  as  a  stepping-stone  to  the  real  study  of  plants  which 
is  presupposed  in  natural  classification. 

Certain  rules  for  division  are  usually  given  in  con- 
nection with  the  treatment  of  this  subject.  It  is  not, 
of  course,  supposed  that  by  their  help  one  can  properly 
divide  any  subject  without  special  knowledge.  The 
purpose  of  these  rules  is  rather  to  warn  against  the 
logical  .errors  to  which  one  is  most  liable  in  the  process 
of  division. 

(1)  Every  division  is  made  on  the  ground  of  differ- 
ences in  some  attribute  (or  attributes)  common  to  all 
the  members  of  the  whole  to  be  divided. 

(2)  Every  division  must  be  based  on  a  single  prin- 
ciple or  ground  (fundamentum  divisionis). 

(3)  The  constituent  species  (or  groups  into  which  the 
whole  is  divided)  must  not  overlap,  but  must  be  mutually 
exclusive. 

(4)  The  division   must  be  exhaustive,   i.e.,  the  con- 
stituent species  must  be  equal,  when  added  together, 
to  the  genus. 

The  first  rule  requires  no  remark.  It  simply  states 
that  it  is  only  possible  to  divide  any  whole  on  the  basis 
of  differences  in  something  which  is  common  to  all  its 
parts.  The  second  rule  warns  against  changing  the 


§  19.     DIVISION  77 

principle  of  division  while  the  process  is  being  carried 
out.  This  law  would  be  violated,  if,  for  example,  one 
were  to  divide  mankind  into  Caucasians,  Negroes,  Mon- 
golians, Europeans,  Australians,  and  Americans.  The 
principle  of  division  which  was  first  adopted  in  this 
example  was  obviously  that  of  the  color  of  the  skin. 
But  this  principle  was  not  carried  through,  and  another 
principle,  that  of  geographical  distribution,  was  substi- 
tuted for  it.  In  dividing  one  must  be  clearly  conscious 
of  the  principle  which  one  is  using,  and  keep  a  firm 
hold  of  it  until  the  division  is  completed.  The  example 
which  we  have  just  given  also  violates  the  third  rule. 
For  not  all  of  the  groups,  European,  Caucasian,  etc., 
exclude  one  another.  Similarly,  it  would  not  be  good 
logic  to  divide  animals  into  vertebrates,  mammals,  in- 
sects, birds,  molluscs,  and  fishes.  The  fourth  rule 
simply  insists  that  the  division  must  be  complete.  The 
whole  must  be  completely  included  in  its  divisions.  It 
would  not  be  a  complete  division  to  say  that  books  may 
be  divided  into  folios,  quartos,  and  duodecimos ;  or 
vertebrates  into  mammals  and  birds.  For  in  neither 
of  these  examples  are  the  divisions  enumerated  equal 
to  the  whole  class. 

References 

J.  S.  Mill,  Logic,  Bk.  I.  Chs.  VII.  and  VIII. 

W.  Minto,  Logic  Inductive  arid  Deductive,  Pt.  II.  pp.  82-130. 

C.  Sigwart,  Logic,  Vol.  I.  §§  42-44. 

J.  H.  Hyslop,  The  Elements  of  Logic,  Ch.  VL 


CHAPTER   VI 

PROPOSITIONS 

§  20.  The  Nature  of  a  Proposition.  —  A  proposition  is 
the  expression  in  words  of  an  act  of  judgment.  It  is 
composed,  as  we  have  already  seen,  of  two  terms,  a 
subject  and  a  predicate,  connected  by  a  copula.  From 
the  point  of  view  of  formal  logic  the  predicate  is  affirmed 
(or  denied)  of  the  subject.  When  we  come  to  consider 
the  nature  of  judgment  (cf.  especially  §§  74,  77),  we 
shall  find  reasons  for  questioning  whether  this  analy- 
sis of  the  proposition  can  be  taken  as  furnishing  a  cor- 
rect account  of  what  actually  takes  place  in  judgment. 
When  we  judge,  we  do  not  begin  with  words  or  terms 
which  are  not  yet  judgments,  and  then  pass  on  to  judg- 
ment by  joining  together  the  former  in  an  external  way. 
The  conclusions'  which  we  shall  have  to  adopt  are,  that 
terms  represent  ways  of  judging,  that  the  simplest 
act  of  thought  is  already  a  judgment,  and  that  thinking 
develops  by  advancing  from  incomplete  to  more  com- 
plete and  comprehensive  judgments.  The  theory  of 
the  syllogism  is,  however,  worked  out  on  the  view  of 
the  proposition  already  indicated.  This  is  sufficiently 
accurate  for  practical  purposes,  and  is  not  likely  to 
lead  to  any  serious  mistakes  so  long  as  we  remember 
that  it  is  the  proposition,  rather  than  the  actual  nature 
of  judgment,  with  which  we  are  dealing. 

78 


§20.    THE  NATURE  OF  A  PROPOSITION  79 

The  logical  proposition,  as  the  expression  of  an  act  of 
thought,  corresponds  to  the  grammatical  sentence.  Not 
every  sentence,  however,  is  a  logical  proposition.  Sen- 
tences which  express  a  wish  or  an  interrogation  do  not 
directly  enter  into  the  process  of  argument  at  all,  and 
may  therefore  be  neglected  for  the  present.  The  same  is 
true  of  exclamatory  sentences.  Again,  even  indicative 
sentences  frequently  require  to  be  rewritten  in  order  to 
reduce  them  to  the  form  of  a  logical  proposition,  which 
demands  two  terms  and  a  copula.  The  sentence,  '  the 
sun  shines,'  must,  therefore,  for  purposes  of  logical 
treatment,  be  reduced  to,  'the  sun  is  a  body  which 
shines.'  '  On  the  hillside  deep  lies  the  snow '  is  ex- 
pressed as  a  logical  proposition  in  some  such  form  as 
this :  '  The  snow  is  a  covering  lying  deep  on  the  hill- 
side.' It  is  very  important  to  change  the  grammatical 
sentence  to  the  regular  form  of  a  proposition  before 
attempting  to  treat  it  logically. 

The  most  general  division  of  propositions  is  that 
which  classifies  them  as  Categorica*  -nd  Conditional.  A 
categorical  proposition  asserts  directly,  and  without  any 
condition.  The  predicate  is  either  affirmed  or  de- 
nied unconditionally  of  the  subject.  'A  is  B,'  'this 
room  is  not  cold,'  '  New  York  is  the  largest  city  in 
America,'  are  examples  of  categorical  propositions. 
Conditional  propositions,  on  the  other  hand,  make  a 
statement  which  is  not  immediately  and  directly  true, 
but  only  claims  to  be  true  under  a  condition ;  as,  e.g., 
'we  shall  go  to-morrow,  if  it  does  not  rain.'  'It  will 
either  rain  or  snow  to-morrow,'  is  also  a  conditional  prop- 
osition ;  for  neither  rain  nor  snow  are  asserted  directly 


80  PROPOSITIONS 

and  absolutely,  but  in  each  case  the  appearance  of  the 
one  is  dependent  upon  the  non-appearance  of  the  other. 
The  first  of  these  conditional  propositions  is  known  as 
a  Hypothetical,  and  the  latter  as  a  Disjunctive  proposi- 
tion ;  but  for  the  present  we  shall  deal  only  with  cate- 
gorical propositions,  and  with  the  form  of  syllogistic 
argument  to  which  they  give  rise.  After  we  have  com- 
pleted the  account  of  the  categorical  syllogism,  however, 
it  will  be  necessary  to  return  to  a  consideration  of 
conditional  propositions,  and  to  the  class  of  arguments 
in  which  they  are  employed. 

§  21.  The  Quality  and  Quantity  of  Propositions.  —  We 
shall  now  consider  the  various  kinds  of  categorical  prop- 
ositions. Such  propositions  are  classified  with  regard  to 
quality  and  quantity.  From  the  standpoint  of  quality, 
propositions  are  either  affirmative  or  negative.  An 
affirmative  proposition  is  one  in  which  an  agreement  is 
affirmed  between  the  subject  and  predicate,  or  in  which 
the  predicate  is  asserted  of  the  subject.  The  proposi- 
tion, 'snow  is  white,'  for  example,  indicates  such  an 
agreement  between  the  subject  and  predicate,  and  is 
therefore  affirmative  in  quality.  A  negative  proposition 
indicates  a  lack  of  agreement  or  harmony  between  the 
subject  and  predicate.  The  predicate  does  not  belong 
to  the  subject,  but  all  relation  or  connection  between  the 
two  is  denied.  'The  room  is  not  cold,'  'the  trees  are  not 
yet  in  full  leaf,'  are  examples  of  negative  propositions. 

The  quantity  of  a  proposition  is  determined  by  the 
extension  of  the  subject.  When  the  proposition  refers 
to  all  of  the  individuals  denoted  by  the  subject,  it  is  said 


§  21.  THE  QUALITY  AND  QUANTITY  OF  PROPOSITIONS       8 1 

to  be  universal  in  quantity.  When,  on  the  other  hand, 
the  proposition  affirms  that  the  predicate  belongs  only 
to  a  part  of  the  subject,  it  is  said  to  be  particular.  For 
example,  '  all  metals  are  elements '  is  a  universal  propo- 
sition, because  the  assertion  is  made  of  the  subject  in 
its  widest  or  fullest  extent ;  '  some  metals  are  white  '  is 
a  particular  proposition,  because  reference  is  made  to 
only  a  part  of  the  subject  'metal.' 

We  divide  propositions,  then,  with  regard  to  quantity, 
into  Universal  and  Particular  propositions.  Universal 
propositions  are  often  indicated  by  adjectives  like  '  all,' 
'the  whole,'  'every/  etc.  It  frequently  happens,  how- 
ever, that  no  such  mark  of  universality  is  present.  A 
scientific  law  is  usually  stated  without  any  explicit 
statement  of  its  quantity,  though  from  its  very  nature  it 
is  meant  to  be  universal.  Thus  we  say,  'the  planets 
revolve  around  the  sun,'  'comets  are  subject  to  the  law 
of  gravitation.'  Propositions  which  have  a  singular  or 
an  individual  name  as  subject  are  often  called  Individual 
propositions,  as,  e.g.,  '  the  earth  is  a  planet,'  '  knowledge 
is  power.'  But  since  it  is  impossible  to  limit  a  singular 
subject,  individual  propositions  are  to  be  regarded  as 
universal.  They  belong,  that  is,  to  the  class  of  propo- 
sitions which  employ  the  subject  term  in  its  complete 
extent. 

Another  class,  called  Indefinite  or  Indesignate  propo- 
sitions, has  sometimes  been  proposed.  This  class  is 
usually  said  to  include  propositions  in  which  the  form 
of  the  words  does  not  give  any  indication  whether  the 
predicate  is  used  of  the  whole,  or  only  of  a  part  of  the 
subject.  '  Men  are  to  be  trusted,'  '  animals  are  capable 


82  PROPOSITIONS 

of  self -movement,'  may  serve  as  examples.  This  classi- 
fication may  be  useful  in  illustrating  the  evil  of  making 
indefinite  or  ambiguous  statements.  Otherwise  there 
is  nothing  to  be  learned  from  it.  A  really  indefinite 
proposition  has  no  place  in  an  argument,  and  logic 
rightfully  refuses  to  deal  with  it.  The  first  demand  of 
logic  is  that  our  statements  shall  be  clear  and  precise. 
A  proposition  is  not  necessarily  indefinite,  however, 
because  it  has  no  qualifying  words  like  'all'  or  'some.' 
It  is  the  meaning  of  a  proposition  as  a  whole,  rather 
than  the  form  of  its  subject,  which  renders  it  definite 
or  indefinite.  Where,  on  the  other  hand,  it  is  really  im- 
possible to  decide  whether  the  proposition  is  universal 
or  particular,  logic  forbids  us  to  proceed  with  the 
argument  until  this  point  has  been  made  clear. 

Particular  propositions  are  usually  preceded  by  some 
word  or  phrase  which  shows  that  the  subject  is  limited 
in  the  extent  of  its  application.  The  logical  sign  of 
particular  propositions  is  'some,'  but  other  qualifying 
words  and  phrases,  such  as  'the  greatest  part,'  'nearly 
all,'  '  several,'  '  a  small  number,'  etc.,  also  indicate  par- 
ticularity. Here  again,  however,  it  is  the  meaning  of 
the  proposition,  rather  than  its  form,  which  is  to  be 
considered.  '  All  metals  are  not  white/  for  example,  is 
a  particular  proposition,  although  introduced  by  'all,' 
since  it  is  clearly  equivalent  to  'some  metals  are  not 
white.'  'Every  mark  of  weakness  is  not  a  disgrace,' 
again,  is  a  particular  proposition,  and  signifies  that  '  not 
all,  or  some  marks  of  weakness  are  not  disgraceful.' 

The  words  'few'  and  'a  few'  require  special  atten- 
tion. The  latter,  as  in  the  proposition,  '  a  few  persons 


§  22.     DIFFICULTIES   IN   CLASSIFICATION  83 

have  spoken  to  me  about  it/  is  equivalent  to  'some,' 
and  introduces  a  particular  affirmative  proposition. 
'  Few,'  on  the  other  hand,  is  negative  in  character. 
Thus,  '  few  were  saved  from  the  shipwreck '  implies  that 
only  a  few  were  saved,  or  that  the  greater  number  did 
not  escape,  and  the  proposition  is  therefore  to  be  con- 
sidered as  a  particular  negative.  Propositions,  then, 
are  classified  as  affirmative  and  negative  in  Quality, 
universal  and  particular  in  Quantity.  When  these  classi- 
fications are  combined,  we  get  four  kinds  of  propositions, 
to  symbolize  which  the  vowels  A,  E,  I,  O  are  employed. 
A  and  I,  the  vowels  contained  in  affirmo,  stand  for 
affirmative  propositions ;  E  and  O,  the  vowels  in  nego, 
for  negative  propositions.  This  may  be  represented  as 
follows :  — 

Affirmative:     All  S  is  P.  A 

Negative:         No  S  is  P.  E 

(    Affirmative :     Some  S  is  P.  I 

:    (    Negative:         Some  S  is  not  P.         O 

We  shall  henceforth  use  A,  E,  I,  and  O  to  represent 
respectively  a  universal  affirmative,  a  universal  negative, 
a  particular  affirmative,  and  a  particular  negative  propo- 
sition. In  dealing  with  propositions  logically,  the  first 
step  is  to  reduce  them  to  one  or  other  of  these  four 
types.  This  can  be  accomplished  readily  by  noticing 
the  distinctions  previously  laid  down.  There  are,  how- 
ever, certain  grammatical  forms  and  sentences  which 
present  some  difficulty,  and  it  may  therefore  be  useful 
to  consider  them  separately. 

§  22.  Difficulties  in  Classification,  —  In  the  first  place, 
we  may  notice  that  in  ordinary  language  the  terms 


Universal   \ 


84  PROPOSITIONS 

of  a  proposition  are  frequently  inverted,  or  its  parts 
separated  in  such  a  way  that  it  requires  attention^  to 
determine  its  true  logical  order.  In  the  proposition, 
'now  came  still  evening  on/  for  example,  the  subject 
'  still  evening '  stands  between  two  portions  of  the 
predicate.  As  a  logical  proposition,  the  sentence  would 
have  to  be  expressed  in  some  such  form  as  the  follow- 
ing :  '  Still  evening  is  the  time  which  now  came  on.' 
Similarly,  we  should  have  to  write  an  inverted  sentence 
like,  '  deep  lies  the  snow  on  the  mountain/  as  '  the  snow 
is  something  which  lies  deep  on  the  mountain.' 

If  a  subject  is  qualified  by  a  relative  clause,  the  verb 
of  the  latter  must  not  be  confused  with  the  main  asser- 
tion of  the  proposition.  Take  the  sentence,  '  he  is  brave 
who  conquers  his  passions.'  Here  it  is  evident  that  the 
relative  clause  describes  or  qualifies  'he.'  Logically, 
then,  the  proposition  is  of  the  form  A,  and  is  to  be 
written,  '  he  who  conquers  his  passions  is  brave/  The 
reader  will  notice  that  all  propositions  which  begin  with 
pronouns  like  'he  who/  'whoever/  etc.,  are  universal 
in  quantity,  since  they  mean  all  who  belong  to  the 
class  in  question. 

(i)  We  have  reduced  grammatical  sentences  to  logical  propo- 
sitions by  changing  the  form  in  such  a  way  as  to  have  two  terms 
united  by  *  is '  or  l  are '  as  the  copula.  Such  a  proposition,  however, 
does  not  express  time,  but  simply  the  relation  existing  between 
subject  and  predicate.  When  the  grammatical  sentence  does 
involve  a  reference  to  time,  and  especially  to  past  or  future  time, 
the  reduction  to  logical  form  is  somewhat  awkward.  Perhaps  the 
best  method  is  to  throw  the  verb  expressing  time  into  the  predi- 
cate. Thus  'the  steamer  will  sail  to-morrow'  =  <the  steamer  is 
a  vessel  which  will  sail  to-morrow ' ;  <  we  waited  for  you  two  hours 


§  23.     RELATION  OF  SUBJECT  AND    PREDICATE        85 

yesterday '  =  '  we  are  persons  who  waited  for  you  two  hours  yes- 
terday.' 

(2)  Exclusive  propositions  exclude  all  individuals  or  classes 
except  those  mentioned  by  the  use  of  some  such  word  as  '  except,' 
'none  but,'  'only.'  'None  but  the  guilty  fear  the  judge';  'only 
citizens  can  hold  property';  'no  admittance  except  on  business.' 
These  propositions  may  all  be  reduced  to  the  form  E  by  writing 
'no'  before  the  negative  of  the  subject  term.  Thus  'none  but  the 
guilty  fear  the  judge '  =  lno  one  who  is  not  guilty  fears  the  judge ' ; 
'only  citizens  can  hold  property'  =  '  no  one  who  is  not  a  citizen, 
etc ' ;  '  no  admittance  except  on  business '  =  '  #0  person  who  has  not 
business  is  to  be  admitted.' 

§  23.   Formal  Relation  of  Subject  and  Predicate.  —  We 

have  now  to  consider  how  the  relation  existing  between 
the  terms  of  a  proposition  is  to  be  understood.  In  §  16 
it  was  shown  that  every  term  may  be  interpreted  in  two 
ways :  either  from  the  point  of  view  of  extension,  or 
from  that  of  intension.  Extensively,  terms  are  taken 
to  represent  objects  or  classes  of  objects ;  while  their 
meaning  in  intension  has  reference  to  the  attributes 
or  qualities  of  things.  Now  the  interpretation  of  the 
categorical  proposition  given  by  formal  logic  is  based 
entirely  on  extension.  That  is,  the  subject  and  predi- 
cate are  regarded  as  standing  for  individual  objects 
or  classes  of  objects.  The  question  to  be  considered, 
then,  concerns  the  extensive  relation  of  these  groups  of 
objects  in  the  propositions  A,  E,  I,  and  O. 

This  mode  of  interpreting  propositions  must  not  be 
taken  as  furnishing  an  adequate  theory  of  the  nature  of 
the  act  of  judgment  which  is  expressed  in  the  proposi- 
tion. It  leaves  entirely  out  of  account,  as  we  have 
seen,  the  connection  of  attributes  asserted  by  the  propo- 


86  PROPOSITIONS 

sition,  which  in  many  cases  is  the  most  prominent 
part  of  its  signification.  Thus  the  proposition,  'all 
metals  are  elements,'  implies  that  the  quality  of  being 
an  element  is  united  with  the  other  qualities  connoted 
by  the  term  'metal.'  Indeed,  this  interpretation  is 
perhaps  more  natural  than  the  one  given  by  formal 
logic,  namely,  that  the  class  of  metals  is  included  in 
the  class  of  elements.  It  must  be  admitted  that  the 
extensive  way  of  reading  propositions,  as  affirming  or 
denying  the  inclusion  of  one  class  of  objects  in  another 
class,  frequently  seems  artificial.  Nevertheless,  it  is 
the  view  upon  which  the  historical  account  of  the 
syllogism  is  founded.  And  the  fact  that  this  mode  of 
representing  the  meaning  of  propositions  leads  in 
practice  to  correct  conclusions,  proves  that  it  is  not 
wholly  false.  It  represents,  as  we  have  seen,  one  side 
or  aspect  of  the  meaning  of  propositions. 

From  the  point  of  view  of  formal  logic,  then,  a  logical 
proposition  signifies  that  a  certain  relation  exists  be- 
tween the  class  of  things  denoted  by  the  subject,  and 
that  denoted  by  the  predicate.  This  relation  may  be 
one  of  inclusion  or  of  exclusion.  For  example,  the  prop- 
osition '  all  good  men  are  charitable '  is  interpreted  to 
mean  that  '  good  men '  are  included  in  the  class  of 
'charitable  men.'  On  the  other  hand,  'no  birds  are 
mammals,'  signifies  that  the  two  classes,  'birds'  and 
'mammals,'  are  mutually  exclusive.  The  meanings  of 
the  four  logical  propositions  A,  E,  I,  and  O  may  be 
represented  by  means  of  a  series  of  diagrams,  which 
were  first  used  by  the  celebrated  German  mathematician 
Euler,  who  lived  in  the  eighteenth  century. 


§  23.     RELATION   OF  SUBJECT  AND   PREDICATE        8? 

To  represent  the  meaning  of  a  proposition  in  A,  like 
1  all  good  men  are  charitable/  we  draw  a  circle  to  sym- 
bolize the  class  of  charitable  beings,  and  then  place 
inside  it  a  smaller  circle  to  stand  for  men.  The  propo- 
sition, that  is,  signifies  that  '  good  men '  are  included  in 
the  class  of  'charitable  beings.'  The  subject  belongs 
to,  or  falls  within,  the  larger  class  of  objects  represented 
by  the  predicate. 


FIG.  i. 

It  must  be  carefully  noted  that  proposition  A  does 
not  usually  assert  anything  of  the  ivhole  of  its  predicate. 
In  the  example  just  given,  no  assertion  is  made  regard- 
ing the  whole  class  of  '  charitable  beings/  but  only  in  so 
far  as  they  are  identical  with  'good  men.'  There  may 
possibly  be  other  charitable  beings  who  are  not  good 
men,  or  not  men  at  all.  The  meaning  of  the  proposition, 
then,  is  that  '  all  good  men  are  some  charitable  beings.' 
In  other  words,  the  predicate  of  the  ordinary  universal 
affirmative  proposition  is  taken  only  in  a  partial,  or 
limited  extent :  nothing  is  affirmed  of  the  whole  of  the 
circle  of  charitable  beings.  We  denote  this  fact  by 
saying  that  the  predicate  of  proposition  A  is  undis* 


88  PROPOSITIONS 

tributed.  The  subject,  on  the  other  hand,  as  a  universal 
term,  is  employed  in  its  fullest  extent,  or  is  distributed. 

In  some  cases,  however,  the  predicate  is  not  a  broader 
term  which  includes  the  subject,  but  the  two  are  equal 
in  extent.  In  the  proposition,  '  all  equilateral  triangles 
are  equiangular,'  for  example,  this  is  the  case.  If  we 
were  to  represent  this  proposition  graphically,  the  circle 
of  equilateral  triangles  would  not  fall  inside  that  of 
equilateral  triangles,  but  would  coincide  with  it.  The 
same  relation  between  subject  and  predicate  holds  in 
the  case  of  logical  definitions.  For  example,  in  the 
definition,  '  monarchy  is  a  form  of  political  government 
where  one  man  is  sovereign,'  the  subject  is  coextensive 
with  the  whole  of  the  predicate.  In  examples  of  this 
kind,  it  is  of  course  obvious  that  the  predicate,  as  well 
as  the  subject,  is  distributed. 

As  an  example  of  proposition  E,  we  may  take  the 
example,  'no  birds  are  mammals.'  The  meaning  of 
this  proposition  is  represented  graphically  by  means 
of  two  circles  falling  outside  each  other  as  in  Fig.  2. 


FIG.  2. 


The  proposition  asserts  that  the  class  of  birds  falls 

completely  without  the  class  of  mammals,  that  the  two 

oj      classes   are   entirely  distinct,   and   mutually   exclusive. 


§  23.     RELATION   OF   SUBJECT  AND   PREDICATE        89 

With  regard  to  quantity,  the  subject  is  of  course  uni- 
versal or  distributed.  And,  in  this  case,  the  predicate  is 
also  distributed.  For  the  proposition  asserts  that  the 
subject  'birds'  does  not  agree  with  any  part  of  'mam- 
mals.' Or,  in  terms  of  the  diagram,  we  deny  that  the 
circle  representing  '  birds  '  corresponds  with  any  portion 
of  the  circle  'mammals.'  But  to  exclude  the  former  circle 
completely  from  the  circle  which  represents  '  mammals,' 
it  is  necessary  that  we  know  the  whole  extent  of  the 
latter.  Otherwise  we  could  not  be  sure  that  the  sub- 
ject had  not  some  point  in  common  with  it.  Proposition 
E,  therefore,  distributes,  or  uses  in  their  widest  extent, 
both  subject  and  predicate. 


FIG.  3. 

The  meaning  of  a  proposition  in  I,  as,  e.g.,  '  some 
birds  are  web-footed,'  is  shown  by  means  of  two  circles 
intersecting  or  overlapping  as  in  Fig.  3.  A  part  of  the 
class  of  birds  corresponds  with  a  part  of  web-footed 
animals.  The  proposition  has  reference  to  the  common 
segment  of  the  two  circles,  which  may  be  large  or  small. 
The  two  circles  correspond  in  part  at  least.  In  proposi- 
tion I,  both  subject  and  predicate  are  undistributed.  The 


9O  PROPOSITIONS 

subject  is,  of  course,  a  particular  or  limited  term.  And, 
as  will  be  clear  from  what  has  already  been  said  in  the 
case  of  proposition  A,  reference  is  made  to  only  a 
limited  portion  of  the  predicate.  In  the  example  used, 
the  assertion  refers  only  to  those  web-footed  animals 
which  are  also  birds.  Or  we  may  say  that  the  proposi- 
tion has  reference  only  to  the  common  segment  of  the 
circles  representing  subject  and  predicate.  Nothing  is 
asserted  of  the  other  portions  of  the  two  circles.  In 
other  words,  both  subject  and  predicate  are  employed 
in  a  limited  extent,  or  are  undistributed. 

'Some  metals  are  not  white,'  may  serve  as  an  example 
of  proposition  O. 


FIG.  4. 

This  proposition  may  be  represented  graphically  as 
in  Fig.  4.  Though  this  is  the  same  form  of  diagram 
as  that  employed  in  the  last  figure,  the  proposition 
refers  now  to  the  outlying  part  of  the  circle  'metals.' 
Some  metals,  it  asserts,  do  not  fall  within  the  sphere  of 
white  substances.  A  larger  or  smaller  section  of  the 
circle  representing  the  former  term,  falls  completely 
"without  the  circle  of  white  substances. 


§  23.     RELATION   OF   SUBJECT  AND   PREDICATE        QI 

It  is  necessary  to  notice  carefully  that  although  the 
subject  of  O  is  undistributed,  its  predicate  is  distributed. 
For,  as  we  have  seen,  a  part  of  the  subject  is  completely 
excluded  from  the  class  of  'white  substances.'  But  in 
order  to  exclude  from  every  part  of  the  predicate,  the 
full  extent  of  the  predicate  must  be  known.  Or,  in 
terms  of  the  diagram,  the  proposition  excludes  a  portion 
of  the  circle  of  metals  (some  metals)  from  each  and 
every  part  of  the  circle  of  white  things.  The  latter 
term  must  therefore  be  used  in  its  full  extent,  or  be 
distributed. 

It  is  absolutely  necessary,  in  order  to  comprehend 
what  follows,  to  understand  the  distribution  of  terms 
in  the  various  propositions.  It  may  help  the  reader  to 
remember  this  if  we  summarize  our  results  in  the  follow- 
ing way  :  — 

Proposition  A,  subject  distributed,  predicate  undistributed. 
Proposition  E,    subject  distributed,  predicate  distributed. 
Proposition   I,  subject  undistributed,  predicate  undistributed. 
Proposition  O,  subject  undistributed,  predicate  distributed. 

References  to  §  23 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  pp.  71-75. 

J.  S.  Mill,  Logic,  Bk.  I.  Ch.  V. 

C.  Sigwart,  Logic,  §  5. 

B.  Bosanquet,  The  Essentials  of  Lo^ic,  Lectures  V.  and  VI. 


CHAPTER  VII 

THE    INTERPRETATION    OF    PROPOSITIONS 

§  24.   The  So-called  Process  of  Immediate  Inference. — 

Many  logicians  speak  of  two  kinds,  or  processes  of  reason- 
ing, to  which  they  give  the  names  of  mediate,  and  imme- 
diate inference.  Mediate  inference,  it  is  said,  asserts 
the  agreement  or  disagreement  of  a  subject  and  predi- 
cate after  having  compared  each  with  some  common 
element  or  middle  term.  The  conclusion  is  thus  reached 
mediately  or  indirectly.  The  syllogism  is  the  best 
example  of  mediate  inference.  In  the  syllogism, 

All  M  is  P, 
All  S  is  M, 
Therefore  S  is  P, 

the  conclusion  is  reached  through  the  medium  of  M, 
with  which  both  S  and  P  have  been  compared.  It  will 
be  noticed  'that  to  obtain  a  conclusion  in  this  way  two 
propositions  or  premises  are  necessary. 

We  sometimes  are  able,  however,  to  pass  directly 
or  immediately  from  one  proposition  to  another.  For 
example,  the  proposition  that  'no  men  are  infallible,' 
warrants  the  statement  that  '  no  infallible  beings  are 
men.'  Or,  if  we  know  that  it  is  true  that '  some  birds  are 
web-footed,'  we  perceive  at  once  that  the  proposition, 
'no  birds  are  web-footed,'  is  false.  It  is  this  process  of 
passing  directly  from  one  proposition  to  another  which 
has  been  named  by  many  logicians  immediate  inference. 

92 


§  24.     PROCESS  OF  IMMEDIATE  INFERENCE  93 

Can  we  be  properly  said  to  infer  at  all  when  we  pass 
from  one  proposition  to  another,  as  in  the  above  ex- 
amples ?  As  we  have  already  shown,  inference  is  a  pro- 
cess of  exhibiting  the  relation  of  facts  to  one  another  by 
discovering  some  common  element,  or  connecting  prin- 
ciple by  means  of  which  they  are  united  (cf.  also  §  87). 
Wherever  we  can  discover  a  connecting  thread,  or  com- 
mon element  between  two  facts  or  groups  of  facts,  we 
are  able  to  infer  with  greater  or  less  certainty  from  the 
nature  of  the  one  what  the  nature  of  the  other  must  be. 
But  it  is  essential  to  inference  that  there  shall  be  a  real 
transition  from  one  fact  to  another  —  that  the  conclu- 
sion reached  shall  be  different  from  the  starting-point. 

The  point  at  issue,  therefore,  is  whether  a  new  fact 
or  truth  is  reached  in  the  so-called  processes  of  imme- 
diate inferences,  or  whether  we  have  the  same  fact 
repeated  in  the  form  of  a  new  proposition.  When  we 
pass  from  'no  men  are  infallible,'  to  '  no  infallible  beings 
are  men/  can  we  be  said  to  infer  a  new  truth  ?  In  this 
case  it  is  evident,  I  think,  that,  there  has  been  no  real 
development  or  extension  of  the  original  proposition 
so  as  to  include  a  new  fact.  The  new  proposition  is  the 
result  of  a  verbal  interpretation  of  the  original  one,  and 
restates  the  same  fact  in  a  different  way.  Inference 
always  completes  or  enlarges  the  truth  from  which  it 
sets  out  by  showing  the  reasons  which  support  it,  or  the 
consequences  which  follow  from  it.  But  when  we  pass 
directly  from  one  proposition  to  another,  as  in  the  exam- 
ples given  above,  it  will  be  found,  I  believe,  that  nothing 
has  really  been  added  to  the  original  statement — no  new 
facts  have  been  brought  into  connection  in  the  process, 


94  THE   INTERPRETATION   OF   PROPOSITIONS 

It  is  of  course  true  that  the  claims  of  each  of  the 
different  types  of  so-called  immediate  inference  should 
be  examined  separately.  But  it  will  be  found,  I  think, 
that  the  conclusion  which  we  have  reached  is  equally 
true  of  all  of  the  forms  to  which  this  name  is  applied. 
It  seems  better  to  regard  these  processes  as  acts  of 
verbal  interpretation,  or  explication  of  the  meaning  of 
propositions,  rather  than  as  inferences  in  the  true  sense 
of  the  word.  They  render  important  service  in  helping 
us  to  understand  what  is  implied  or  involved  in  the 
propositions  we  use,  but  they  do  not  lead  the  mind  on 
to  any  new  truth.  We  may  consider  three  ways  in 
which  propositions  may  be  transformed  as  a  result  of 
the  interpretative  process  —  Opposition,  Obversion,  and 
Conversion. 

§  25.  The  Opposition  of  Propositions,  —  We  have  seen 
that  all  categorical  propositions  have  to  be  reduced  to 
one  of  the  four  forms,  A,  E,  I,  O,  in  order  to  be  dealt 
with  by  logic.  Now,  when  these  propositions  have  the 
same  subject  and  predicate,  certain  relations  exist  be- 
tween them,  to  which  the  general  name  of  Opposition 
has  been  given.  It  is  clear  that  the  truth  of  some  of 
these  propositions  interferes  with  the  truth  of  others. 
Thus  if  it  be  true  that  'no  professional  gamblers  are 
honest,'  it  is  impossible  that  '  all  professional  gamblers 
are  honest,'  or  even  that  some  are  honest.  The  propo- 
sition E  is  thus  inconsistent  with  both  A  and  I.  Again, 
if  it  be  false  that '  all  politicians  are  dishonest,'  it  must  be 
true  that  '  some  politicians  are  not  dishonest,'  though  it 
by  no  means  follows  that  '  no  politicians  are  dishonest,' 


§  25.    THE  OPPOSITION   OF  PROPOSITIONS 


95 


That  is,  when  A  is  false,  O  is  necessarily  true,  while  E 
may  or  may  not  be  true.  Propositions  A  and  E  are 
called  contrary  propositions.  'All  A  is  B,'  and  'no  A 
is  B,'  express  the  greatest  possible  degree  of  contrariety 
or  opposition.  If  one  proposition  be  true,  the  other  is 
necessarily  false.  It  is  to  be  noticed,  however,  that  we 
cannot  conclude  that  if  one  is  false,  the  other  is  true. 
For  both  A  and  E  may  be  false.  Thus,  for  example, 
the  propositions,  'all  men  are  wise/  and  'no  men  are 
wise,'  are  both  false.  But,  on  the  other  hand,  proposi- 
tions A  and  O,  E  and  I,  are  pairs  of  contradictory  prop- 
ositions :  if  one  is  false,  its  contradictory  is  necessarily 
true ;  and  if  one  is  true,  the  other  is  manifestly  false. 

The  relation  of  the  four  logical  propositions  is  clearly 
shown  by  arranging  them  in  the  following  way :  — 

A  Contraries  P 


Sub-Contraries 

FIG.  5. 


96  THE  INTERPRETATION  OF  PROPOSITIONS        v 

A  and  E  are  known  as  contraries ;  I  and  O  as  sub- 
contraries  ;  A  and  O,  I  and  E,  as  contradictories ;  A 
and  I,  E  and  O,  are  subalterns. 

The  relations  of  these  propositions  may  now  be 
summed  up  in  the  following  statements :  — 

(1)  Of  contrary  propositions,  one  is  false  if  the  other 
is  true,  but  both  may  be  false. 

(2)  Of  contradictory  propositions,  one  is  true  and  the 
other  necessarily  false. 

(3)  If  a  universal  proposition  is  true,  the  particular 
which  stands  under  it  is  also  true ;  but  if  the  universal 
is  false,  the  particular  may  or  may  not  be  true. 

(4)  If  a  particular  proposition  is  true,  the  correspond- 
ing universal  may  or  may  not  be  true ;  but  if  the  par- 
ticular is  false,  the  universal  must  be  false. 

(5)  Subcontrary  propositions  may  both  be  true;  but 
if  one  is  false,  the  other  is  necessarily  true. 

The  knowledge  that  any  one  of  these  propositions  is 
either  true  or  false  enables  us  to  determine  the  truth  or 
falsity  of  at  least  some  of  the  others. 

For  example,  if  A  is  true,  E  is  false,  O  is  false,  and 
I  is  true.  If  A  is  false,  E  is  doubtful,  O  is  true,  and 
I  doubtful. 

If  I  is  true,  E  is  false,  A  is  doubtful,  and  O  doubtful. 
If  I  is  false,  E  is  true,  A  is  false,  and  O  true. 

Similarly  we  are  also  able  to  determine  what  follows 
when  we  suppose  that  E  and  O  are  either  false  or  true. 

It  ought  to  be  carefully  noted  that  when  we  affirm  the  truth  of 
the  particular  proposition  I,  we  do  not  deny  the  truth  of  the  universal 
proposition  A.  The  proposition,  'some  students  are  fond  of  recre- 
ation,' for  example,  does  not  exclude  the  truth  of  *  all  students  an* 


§  25.    THE  OPPOSITION   OF  PROPOSITIONS  97 

fond  of  recreation.'  Similarly,  the  truth  of  O  does  not  exclude  the 
corresponding  proposition  in  E  :  the  statement,  *  some  men  are  not 
generous,'  for  example,  does  not  interfere  with  the  truth  of  the  uni- 
versal proposition,  '  no  men  are  generous.'  A  particular  proposition, 
in  other  words,  asserts  something  of  a  limited  part  of  a  subject; 
it  neither  affirms  nor  denies  anything  of  the  same  term  taken 
universally. 

The  reader  will  remember  that  propositions  which 
have  the  name  of  some  singular  or  individual  thing  as 
subject,  have  been  classified  as  universal.  '  New  York 
is  the  largest  city  in  America,'  '  charity  is  not  the  only 
virtue,'  are  examples  of  such  propositions.  Now  it  is  at 
once  evident  that  in  cases  of  this  kind  there  are  no  cor- 
responding particular  propositions.  What  has  just  been 
said  regarding  the  relation  of  universal  and  particular 
propositions,  applies  therefore  only  to  propositions  which 
have  a  general  term  or  name  as  subject.  Moreover, 
we  must  notice  that  when  A  and  E  propositions  have 
a  singular  or  individual  name  as  subject,  the  relations 
between  them  are  somewhat  different  from  those  just 
stated.  A  arid  E,  we  said,  are  contrary,  but  not  contra- 
dictory propositions.  By  that  it  was  implied  that  al- 
though we  can  proceed  from  the  truth  of  the  one  to  the 
falsity  of  the  other,  it  is  not  possible  to  go  in  a  converse 
direction,  from  falsity  to  truth.  We  cannot  conclude, 
for  example,  from  the  falsity  of  the  proposition  that 
1  all  men  are  selfish '  the  truth  of  the  corresponding 
negative  proposition,  (  no  men  are  selfish.'  With  contra- 
dictory propositions,  however,  we  can  go  from  a  denial 
to  an  affirmation.  Now  the  point  to  be  observed,  with 
regard  to  propositions  with  a  singular  term  as  subject, 
H 


98  THE  INTERPRETATION   OF  PROPOSITIONS 

is  that  although  only  contraries  in  form,  they  have  yet 
the  force  of  contradictories.  *  Socrates  is  wise '  (A), 
and  '  Socrates  is  not  wise  '  (E),  are  contradictory  as  well 
as  contrary,  propositions. 

§  26.  The  Obversion  of  Propositions,  —  The  terms  '  Ob- 
version  '  and  '^Equipollence '  were  formerly  used  to 
denote  any  process  by  which  the  form  of  a  proposition 
is  changed  without  an  alteration  in  meaning  being, 
involved.  The  name  *  Obversion '  is,  however,  now  gen- 
erally employed  to  describe  the  change  which  a  propo- 
sition undergoes  in  passing  from  the  affirmative  to  the 
negative,  or  from  the  negative  to  the  affirmative  form 
while  still  retaining  its  original  meaning. 

Every  fact  is  capable  of  expression  either  in  the  form 
of  an  affirmative  or  of  a  negative  proposition.  Whether 
the  affirmative  or  negative  form  is  chosen  in  any  par- 
ticular case,  is  partly  a  matter  of  convenience.  It  is 
also  determined  largely  by  the  psychological  interest  of 
the  moment,  i.e.,  by  the  purpose  which  we  have  in  view 
in  making  the  assertion.  When,  for  example,  we  wish 
to  repel  some  suggestion  which  may  have  occurred  to 
us,  or  to  deny  something  which  our  companions  appear 
to  believe,  we  naturally  choose  the  negative  form  of 
statement.  But  the  meaning  of  the  proposition  is  the 
same  whether  we  say,  'all  men  are  fallible/  or,  'no  men 
are  infallible.'  Similarly,  we  can  say,  'not  one  of  the 
crew  escaped,'  or,  '  all  of  the  crew  perished/ 

Obversion,  then,  is  the  process  of  substituting  for 
any  affirmative  proposition  its  equivalent  in  negative 
form,  or  of  expressing  the  meaning  of  a  negative  prop- 


§  26.    THE  OBVERSION  OF  PROPOSITIONS  99 

osition  as  an  affirmative.  To  obtain  the  obverse  of 
proposition  A,  we  proceed  on  the  principle  that  two 
negatives  are  equal  to  an  affirmative.  Instead  of  'all 
animals  digest  food,'  we  may  write,  'no  animals  are 
beings  that  do  not  digest  food';  for,  'every  man  has 
his  own  troubles,'  '  there  are  no  men  who  have  not 
their  own  troubles.'  Instead  of  affirming  the  predicate 
of  the  subject,  the  obverse  of  A  takes  the  negative  of 
the  original  predicate  and  denies  it  universally. 

Proposition  I  may  be  obverted  in  the  same  way, 
though  it  yields  a  particular,  instead  of  a  universal 
negative  proposition.  Thus  the  obverse  of,  '  some  of 
the  houses  are  comfortable,'  is  '  some  of  the  houses  are 
not  not-comfortable,'  i.e.,  uncomfortable.  We  deny  the 
negative  predicate  in  the  obverse  proposition,  instead  of 
affirming  the  positive. 

We  obtain  the  obverse  of  the  propositions  E  and  O 
by  changing  the  negation  contained  in  them  to  its 
equivalent  affirmation.  This  is  done  by  attaching  the 
negative  to  the  predicate,  and  then  affirming  it  of  the 
subject.  For  example,  to  obtain  the  obverse  of,  '  no  one 
who  was  present  can  forget  the  scene,'  we  first  write  the 
proposition  in  logical  form,  *  no  one  who  was  present  is  a 
person  who  can  forget  the  scene.'  Now  the  negative  of 
the  predicate  term,  'a  person  who  can  forget  the  scene/ 
is,  '  a  person  who  can  not  forget  the  scene/  Affirming 
this  universally  we  get,  '  all  persons  who  were  present 
are  persons  who  cannot  forget  the  scene/  As  an  exam- 
ple of  how  the  obverse  of  O  is  obtained,  we  may  take  the 
proposition,  'some  metals  are  not  white.'  Now  if  we 
change  the  quality  of  the  proposition  by  attaching  the 


IOO  THE  INTERPRETATION  OF   PROPOSITIONS/ 

negative  to  the  predicate,  we  obtain  '  some  metals  are  not- 
white.'  That  is,  instead  of  denying,  we  affirm  the  neg- 
ative of  the  original  predicate.  When  the  predicate  is 
made  up  of  several  words,  it  is  important  that  the  logical 
contradictory  of  the  whole  term  be  taken.  For  example, 
in  the  proposition,  '  some  men  are  not  fond  of  work,'  the 
predicate  fully  expressed  is,  '  persons  who  are  fond  of 
work.'  Now  the  negative  or  contradictory  term  corre- 
sponding to  this  is,  '  persons  who  are  not  fond  of  work.' 
The  obverse  of  the  original  proposition  therefore  is, 
'some  men  are  persons  who  are  not  fond  of  work.' 

§  27.  The  Conversion  of  Propositions.  —  To  convert  a 
proposition  is  to  transpose  its  subject  and  predicate  so 
that  each  shall  occupy  the  place  previously  held  by  the 
other.  Thus  the  proposition,  '  no  men  are  infallible,'  is 
converted  by  writing  it,  'no  infallible  beings  are  men.' 
The  original  proposition  is  called  the  convertend,  and  the 
proposition  obtained  by  conversion  the  converse.  By 
conversion,  then,  a  new  proposition  is  derived  directly 
from  an  old  one.  It  is  for  this  reason  that  conversion  is 
usually  ranked  as  a  process  of  immediate  inference. 
But,  as  we  have  already  seen,  the  process  of  interpreta- 
tion which  results  in  conversion  seems  to  fall  wholly 
within  the  proposition.  In  other  words,  it  makes  clear 
what  is  involved  in  the  original  proposition,  but  does  not 
lead  to  any  new  fact  with  which  the  latter  is  connected. 
We  therefore  reached  the  conclusion  that  it  might  more 
properly  be  regarded  as  a  process  of  formal  interpreta- 
tion, than  as  one  which  involves  real  inference. 

It  is  evident  that  in  proceeding  to  convert  propositions 


§  27.    THE   CONVERSION  OF   PROPOSITIONS  IOI 

it  will  be  necessary  to  notice  whether  the  predicate  of 
the  convertend,  or  proposition  to  be  converted,  is  dis- 
tributed or  undistributed,  otherwise  we  should  not  know 
what  extension  to  apply  to  this  term  when  used  as 
the  subject  of  the  converse  proposition.  The  rules 
usually  given  to  limit  the  process  of  conversion  are  as 
follows :  — 

(1)  No  term  must  be  distributed  in  the  converse  prop- 
osition which  was  not  distributed  in  the  convertend. 

(2)  The   quality  of   the   converse   proposition    must 
remain  the  same  as  the  quality  of  the  convertend. 

The  reason  for  the  first  rule  is  at  once  evident  from 
what  has  been  already  said.  The  second  rule  is  not  one 
which  is  always  observed.  Of  course,  the  meaning  of 
a  proposition  must  not  be  altered  by  changing  the  qual- 
ity simply  or  directly.  But,  in  converting  by  Contrapo- 
sition, as  we  shall  see  later,  it  is  first  necessary  to  obtain 
the  equivalent  of  the  convertend  by  obversion,  and  this 
necessarily  involves  a  change  of  quality. 

There  are  three  kinds  of  conversion  usually  recog- 
nized :  (a)  Simple  Conversion ;  (£)  Conversion  by  Limi- 
tation or  per  accidens ;  (c)  Conversion  by  Contraposition. 

(a)  By  Simple  Conversion  is  meant  the  direct  trans- 
position of  the  subject  and  predicate  without  any  other 
change  in  the  form  of  the  proposition.  Both  propositions 
E  and  I  can  be  converted  in  this  way.  Thus  the 
converse  of,  '  none  of  the  books  on  this  shelf  are  novels,' 
is  another  proposition  in  E,  '  no  novels  are  books  on  this 
shelf.'  From  '  some  dicotyledons  are  exogens  '  we  obtain 
by  conversion  another  particular  affirmative  proposition, 
*  some  exogens  are  dicotyledons/ 


102  THE  INTERPRETATION  OF  PROPOSITIONS 

/ 

(#)  Conversion  by  Limitation  or  per  accidens  is  applied 
to  proposition  A.  In  this  process  A  loses  its  univer- 
sality, and  yields  as  a  result  only  proposition  I.  To 
illustrate  this  mode  of  conversion  we  may  take  the  propo- 
sition, 'brown  hematite  is  an  iron  ore.'  As  we  already 
know,  the  term  'an  iron  ore,'  being  the  predicate  of 
proposition  A,  is  undistributed.  When  used  as  the  sub- 
ject of  a  new  proposition,  therefore,  it  must  be  limited 
by  the  adjective  'some.'  We  thus  obtain  the  converse 
proposition,  'some  iron  ore  is  brown  hematite.'  Simi- 
larly, the  converse  of  the  proposition,  '  all  sensations  are 
mental  processes,'  is  'some  mental  processes  are  sensa- 
tions.' When  proposition  A  is  converted  by  limitation, 
then,  it  yields  proposition  I  as  a  result.  And  it  is  evident 
that  the  proposition  has  really  lost  something  in  the 
process.  For  it  is  impossible  by  converting  again  to 
obtain  anything  more  than  a  particular  proposition. 
It  is,  however,  sometimes  possible  to  convert  proposition 
A  without  limiting  the  predicate.  In  formal  definitions, 
for  example,  the  subject  and  the  predicate  are  of  equal 
extent,  and  may  be  transposed  simply  without  any 
limitation  of  the  latter.  Thus  the  converse  of,  'an 
equilateral  triangle  is  a  plane  figure  having  three  equal 
sides,'  is  '  a  plane  figure  having  three  equal  sides  is  an 
equilateral  triangle.' 

(c)  In  Conversion  by  Contraposition  the  negative  or 
contradictory  of  the  original  predicate  is  taken  as  the 
subject  of  the  converse  proposition.  This  method  of 
conversion  is  usually  applied  only  to  propositions  A 
and  O. 

When  applied  to  A,  it  means  that  from  a  proposition 


§  27.    THE  CONVERSION  OF  PROPOSITIONS  103 

in  the  form,  All  B  is  C,  we  are  able  to  assert  something 
of  what  is  not  C.  If  we  know,  for  example,  that  '  all 
the  planets  are  bodies  revolving  around  the  sun,'  we 
can  obtain  by  contraposition  the  proposition,  '  no  bodies 
which  do  not  revolve  around  the  sun  are  planets.'  The 
rule  for  contraposition  is,  first  obvert,  and  then  convert 
simply.  Thus,  the  obverse  of,  'aluminium  is  a  white 
metal,'  is  the  proposition  in  E,  'aluminium  is  not  a 
metal  which  is  not  white;'  .and  converting  this  simply, 
we  get  as  the  contrapositive  of  the  proposition  from 
which  we  started,  'no  metal  which  is  not  white  is  alu- 
minium.' 

Proposition  O  can  be  converted  only  by  contraposi- 
tion. If  we  were  to  convert  simply,  as,  e.g.,  '  some 
metals  are  not  white,'  'some  white  things  are  not 
metals,'  we  should  fall  into  error ;  for  the  term  '  metal ' 
is  distributed  in  the  converse  proposition  without  having 
been  distributed  in  the  convertend. 

To  obtain  the  converse  of  O  by  contraposition,  the 
rule  given  above,  first  obvert  and  then  convert  simply, 
applies  once  more.  The  obverse  of  the  proposition  in 
O,  '  some  men  who  make  loud  professions  are  not  to  be 
trusted,'  is  the  equivalent  in  I,  'some  men  who  make 
loud  professions  are  persons  not  to  be  trusted.'  Con- 
verting this  simply,  we  obtain  the  contrapositive,  '  some 
persons  not  to  be  trusted  are  men  who  make  loud  pro- 
fessions.' 

For  the  sake  of  convenience  we  may  sum  up  the 
treatment  of  Conversion  as  follows :  — 


104  THE  INTERPRETATION  OF  PROPOSITIONS 

Proposition  A  is  converted  (i)  by  Limitation,  and  (2)  by  Contra- 
position. 

All  S  is  P.        (A) 

(1)  Converting  by  Limitation,  Some  P  is  S.     (I) 

i.)  Obversion  yields,  No  S  is 

(2)  Converting  by  Contraposition  j  .. 

11.)  The  Simple  Converse  of  this 

I  is,  No  not-P  is  S.    (E) 

Proposition  I  is  converted  Simply. 

Some  S  is  P.     (I) 
Converting  Simply,  Some  P  is  S.     (I) 

Proposition  E  is  converted  Simply. 

No  S  is  P.     (E) 
Converting  Simply,  No  P  is  S.     (E) 

Proposition  E  may  also  be  converted  by  Contraposition,  but  the 
result  is  the  same  as  the  Contrapositive  of  O.     Thus  for  example  :  — 

No  S  is  P.     (E) 

i.)  Obversion  yields,  All  S  is  not- 

P.  (A) 

ii.)  Converting  this  by  Limitation, 

Some  not-P  is  S.      (I) 


Converting  by  Contraposition 


Proposition  O  is  converted  by  Contraposition. 
Some  S  is  not  P.     (O) 

f  i.)  Obversion   yields,    Some   S   is 

not-P.  (I) 

Converting  by  Contraposition  \         —,-,.,«  r    ,- 

ii.)  The  Simple   Converse  of  this 

i  is,  Some  not-P  is  S.      (I) 

References 

B.  Bosanquet,  Logic,  Vol.  I.  pp.  310-319. 

W.  Minto,  Logic  Inductive  and  Deductive,  Pt.  III.  pp.  130-166. 

J.  H.  Hyslop,  The  Elements  of  Logic,  Ch.  X. 


CHAPTER  VIII 

THE    SYLLOGISM 

§  28.  The  Nature  of  Syllogistic  Reasoning.  — The  syl- 
logism, as  we  have  already  seen  (§  10),  presents  a  con- 
clusion together  with  the  reasons  by  means  of  which 
it  is  supported.  A  single  proposition  taken  by  itself 
is  dogmatic  :  it  merely  asserts  without  stating  the  grounds 
upon  which  it  rests.  The  syllogism,  on  the  other  hand, 
justifies  its  conclusion  by  showing  the  premises  from 
which  it  has  been  derived.  It  thus  appeals  to  the 
reason  of  all  men,  and  compels  their  assent.  To  do 
this,  it  is  of  course  necessary  that  the  truth  of  the 
premises  to  which  appeal  is  made  should  be  granted. 
If  the  premises  are  disputed  or  doubtful,  the  argument 
is  pushed  a  step  further  back,  and  it  is  first  necessary 
to  show  the  grounds  upon  which  these  premises  rest. 
The  assumption  of  syllogistic  reasoning  —  and,  indeed, 
of  all  reasoning  whatsoever  —  is  that  it  is  possible  to 
reach  propositions  which  every  one  will  accept.  There 
are  certain  facts,  we  say,  well  known  and  established, 
and  these  can  always  be  appealed  to  in  support  of  our 
conclusions.  In  syllogistic  reasoning,  then,  we  exhibit 
the  interdependence  of  propositions ;  i.e.,  we  show  how 
the  truth  of  some  new  proposition,  or  some  proposition 
not  regarded  as  beyond  question,  follows  necessarily 

105 


106  THE  SYLLOGISM 

from  other  propositions  whose  truth  every  one  will 
admit. 

The  question  which  arises  in  connection  with  the 
syllogism,  therefore,  is  this :  Under  what  conditions 
do  propositions  which  are  accepted  as  true  contain  or 
imply  a  new  proposition  as  a  conclusion  ?  Or  we  may 
put  the  question  in  this  form :  In  what  ways  may  the 
four  logical  propositions,  A,  E,  I,  O,  be  combined  so  as 
to  yield  valid  conclusions  ? 

We  pointed  out  in  a  previous  chapter  that  a  syllogism 
has  alway^  two  premises.  It  is,  however,  impossible  to 
obtain  a  conclusion  by  combining  any  two  propositions 
at  random,  as  e.g.,  — 

All  A  is  B. 

No  X  is  Y. 

It  is  evident  that  any  two  propositions  will  not  yield  a 
conclusion  by  being  taken  together.  In  order  to  serve 
as  premises  for  a  syllogism,  propositions  must  fulfil 
certain  conditions,  and  stand  in  certain  definite  relations 
to  each  other.  To  determine  some  of  the  most  apparent 
of  these  conditions,  let  us  examine  the  argument :  — 

All  mammals  are  vertebrates, 
The  whale  is  a  mammal, 
Therefore  the  whale  is  a  vertebrate. 

It  will  be  noticed  that  the  term  '  mammal '  is  common 
to  both  premises,  and  that  it  does  not  occur  at  all  in  the 
conclusion.  Moreover,  it  is  because  the  other  terms 
are  compared  in  turn  with  this  common  or  Middle  Term 
and  found  to  agree  with  it,  that  they  can  be  united  in 
the  conclusion.  It  is  only  propositions  which  have  a 
middle  term,  therefore,  which  can  be  employed  as  the 


§  28.    THE  NATURE  OF  SYLLOGISTIC  REASONING 

premises  of  a  syllogism.  The  syllogism  is  thus  essen- 
tially a  process  of  comparison.  Each  of  the  terms 
entering  into  the  conclusion  is  compared  in  turn  with 
the  same  middle  term,  and  in  this  way  their  relation 
to  each  other  is  determined.  We  reach  the  conclusion 
not  directly  or  immediately,  but  by  means  of  the  middle 
term.  The  conclusion  is  therefore  said  to  be  mediated, 
and  the  process  itself  is  sometimes  called  mediate 
reasoning. 

It  will  be  interesting  to  compare  what  has  just  been  said  regard- 
ing the  function  of  the  middle  term,  with  what  has  been  previously 
stated  regarding  the  nature  of  inference.  When  we  infer  one  fact 
from  another,  it  was  said,  we  do  so  by  discovering  some  identical  link 
or  connecting  thread  which  unites  both.  We  may  say  that  to  infer 
is  to  see  that,  in  virtue  of  some  identical  link  which  our  thought  has 
brought  to  light,  the  two  facts,  or  groups  of  facts,  are  in  a  certain 
sense  identical.  Now  the  middle  term  in  a  syllogism  is  just  the 
explicit  statement  of  the  nature  of  this  identical  link.  It  is  true  that 
in  the  syllogism  we  seem  to  be  operating  with  words  or  terms  rather 
than  with  the  thought-process  itself.  When  we  go  behind  the 
external  connection  of  the  terms,  however,  we  can  see  that  the  middle 
term  represents  the  universal  principle,  by  means  of  which  the  con- 
clusion is  reached.  In  the  example  given  above,  for  instance,  we 
reason  that  the  whale,  being  a  mammal,  is  a  vertebrate. 

The  terms  which  enter  into  the  conclusion  of  a 
syllogism  are  sometimes  called  the  Extremes,  as  opposed 
to  the  middle  term.  Of  the  Extremes,  the  predicate  of 
the  conclusion  is  known  as  the  Major  Term,  and  the  sub- 
ject of  the  conclusion  as  the  Minor  Term.  The  premise 
which  contains  the  major  term  is  called  the  Major  Premise, 
and  stands  first  when  the  syllogism  is  arranged  in  logical 
form.  The  Minor  Premise,  on  the  other  hand,  is  the 


108  THE  SYLLOGISM 

premise  which  contains  the  minor  term,  and  stands 
second  in  the  arrangement  of  the  syllogism.  The  prop- 
ositions of  which  the  syllogism  is  composed  may  occur, 
however,  in  any  order  in  actual  reasoning;  either 
premise,  or  even  the  conclusion,  may  stand  first.  To 
arrange  an  argument,  therefore,  it  is  necessary  to 
determine  which*  is  the  major,  and  which  the  minor 
premise.  This  can  be  done  only  by  turning  to  the 
conclusion,  and  distinguishing  the  major  and  minor 
terms.  For  example,  take  the  syllogism  :  — 

The  whale  suckles  its  young, 
No  fish  suckles  its  young, 
Therefore  the  whale  is  not  a  fish. 

By  turning  to  the  conclusion  we  see  that  '  fish '  (being 
the  predicate)  is  the  major  term.  The  proposition 
which  contains  this  term,  'no  fish  suckles  its  young,' 
is,  therefore,  the  major  premise,  and  should  stand  first. 
Before  proceeding  to  examine  the  syllogism  further 
it  would  be  necessary  to  arrange  it  as  follows :  — 

No  fish  is  an  animal  which  suckles  its  young, 
The  whale  is  an  animal  which  suckles  its  young, 
Therefore  the  whale  is  not  a  fish. 

§  29.  The  Rules  of  the  Syllogism,  —  It  is  customary 
to  give  a  number  of  rules  or  canons  to  which  the  syl- 
logism must  conform  in  order  to  yield  valid  conclusions. 
We  shall  first  enumerate  the  rules,  and  afterwards 
remark  on  their  meaning  and  importance. 

(i)  In  every  syllogism  there  should  be  three,  and 
only  three,  terms,  and  these  terms  must  be  used 
throughout  in  the  same  sense. 


§  29.    THE   RULES   OF  THE   SYLLOGISM  1 09 

The  terms,  as  we  have  already  remarked,  are  known 
as  the  major  term,  the  middle  term,  and  the  minor  term. 

(2)  Every  syllogism  contains  three,  and  only  three, 
propositions. 

These  are  called  the  major  premise,  minor  premise, 
and  conclusion. 

(3)  The  middle  term  must  be  distributed  in  at  least 
one  of  the  premises. 

(4)  No  term   must  be  distributed  in  the  conclusion 
which  was  not  distributed  in  one  of  the  premises.     - 

(5)  From  negative  premises  nothing  can  be  inferred. 

(6)  If  one  premise  be  negative,  the  conclusion  must 
be  negative ;  and,  conversely,  to  prove  a  negative  con- 
clusion one  of  the  premises  must  be  negative. 

As  a  consequence  of  the  above  rules  there  result  two 
additional  canons  which  may  be  set  down  here. 

(/)  No  conclusion  can  be  drawn  from  two  particular 
premises. 

(8)  If  one  of  the  premises  be  particular,  the  conclu- 
sion must  be  particular. 

The  reason  for  the  first  and  second  rules  will  be 
evident  from  what  has  been  already  said  about  the  struct- 
ure of  the  syllogism.  We  saw  that  a  logical  argument 
is  a  process  of  comparison ;  that  two  terms  are  united 
through  comparing  them  with  a  common  or  middle 
term.  If  the  meaning  of  the  terms  does  not  remain 
fixed,  there  are  more  than  three  terms,  and  no  com- 
parison is  possible.  The  second  rule  follows  as  a  corol- 
lary from  the  first. 

The  third  rule,  that  the  middle  term  must  be  dis- 
tributed once,  at  least,  is  extremely  important,  and  its 


110  THE  SYLLOGISM 

necessity  will  be  readily  perceived.  For,  since  the 
middle  term  is  the  standard  of  comparison,  it  must  be 
used  in  at  least  one  premise  in  its  universal  extent. 
Otherwise  we  might  compare  the  major  term  with  one 
part  of  it,  and  the  minor  term  with  another  part.  Such 
a  comparison  would  of  course  not  warrant  us  in  either 
affirming  or  denying  the  connection  of  these  terms  in 
the  conclusion.  For  example,  the  two  propositions, 

Sedimentary  rocks  are  stratified  substances, 
Some  metamorphic  rocks  are  stratified  substances, 

do  not  distribute  the  middle  term,  '  stratified  sub- 
stances,' at  all,  being  both  affirmative  propositions.  It 


FIG.  6. 

is  clear  that  the  term,  '  sedimentary  rocks/  agrees  with 
one  part  of  the  stratified  substances,  and  '  metamorphic 
rocks'  with  another  part.  We  are,  therefore,  not  able 
to  infer  that  '  some  metamorphic  rocks  are  sedimentary 
rocks/  This  may  be  clearly  shown  by  representing  the 
propositions  by  Euler's  method  of  circles  as  in  Fig.  6. 
We  know  from  the  second  proposition  that  the  circle 
representing  '  metamorphic  rocks '  falls  partly  within  the 


§29.    THE   RULES   OF  THE  SYLLOGISM  III 

circle  of  '  stratified  substances.'  But  it  is  impossible  to 
determine  from  the  statement  whether  it  corresponds  at 
all  with  the  circle  of  sedimentary  rocks,  or  falls,  as  in 
the  figure,  entirely  without  it. 

The  fourth  rule  states  that  no  term  must  be  dis- 
tributed in  the  conclusion  which  was  not  distributed  in 
one  of  the  premises.  That  is,  the  conclusion  must  be 
proved  by  means  of  the  premises,  and  no  term  which 
was  not  employed  in  its  universal  signification  in  the 
premises  can,  therefore,  be  used  universally  or  dis- 
tributively  in  the  conclusion.  This  rule  may  be  violated 
by  using  either  the  major  or  the  minor  term  in  a  wider 
sense  in  the  conclusion  than  in  the  premise  in  which  it 
occurs.  The  resulting  fallacies  are  then  known  as  the 
Illicit  Process  of  the  major  and  minor  terms  respec- 
tively. As  an  illustration  of  the  illicit  process  of  the 
major  term,  we  may  consider  the  following  argument :  — 

All  rational  beings  are  responsible  for  their  actions, 
Brutes  are  not  rational  beings, 

Therefore  brutes  are  not  responsible  for  their  actions. 

It  will  be  at  once  seen  that  the  major  term,  'beings 
responsible  for  their  actions,'  is  distributed  in  the  con- 
clusion, but  was  not  distributed  when  it  appeared  as  the 
predicate  of  an  affirmative  proposition  in  the  major 
premise.  The  fallacious  nature  of  this  argument  may 
also  be  shown  by  representing  the  proposition  by 
circles. 

The  illicit  process  of  the  minor  term  is  usually  more 
easily  detected.  We  may  take  as  an  example  of  this 
fallacy :  — 


112  THE  SYLLOGISM 

All  good  citizens  are  ready  to  defend  their  country, 

All  good  citizens  are  persons  who  vote  regularly  at  elections. 

Therefore  all  who  vote  regularly  at  elections  are  ready  to  defend 
their  country. 

It  is  clear  that  the  minor  term,  'persons  who  vote 
regularly  at  elections,'  is  undistributed  when  used  as 
the  predicate  of  the  minor  premise.  In  the  conclusion, 
however,  it  is  wrongly  taken  universally,  and  it  is  this 
unwarranted  extension  to  which  the  name  of  illicit 
minor  is  given.  Students  are  advised  to  draw  circles 
to  illustrate  the  nature  of  this  fallacy. 

The  fifth  and  sixth  rules  have  reference  to  negative 
premises.  It  is  not  difficult  to  understand  why  two 
negative  premises  cannot  yield  any  conclusion.  For, 
from  the  fact  that  S  and  P  are  both  excluded  from  M,  we 
can  conclude  nothing  regarding  their  relation  to  each 
other.  Two  negative  premises  afford  us  no  standard  by 
means  of  which  we  can  determine  anything  concerning 
the  relation  of  major  and  minor  terms.  Again,  where 
one  premise  is  negative  and  the  other  affirmative,  it  is 
asserted  that,  of  the  major  and  minor  terms,  one  agrees, 
and  the  other  does  not  agree,  with  the  middle  term. 
The  necessary  inference  from  these  premises,  then,  is 
that  major  and  minor  terms  do  not  agree  with  each 
other.  That  is,  the  conclusion  must  be  negative. 

It  is  worth  noticing  that  it  is  sometimes  possible  to  obtain  a  con- 
clusion from  premises  which  are  both  negative  in  form.  For  ex- 
ample :  — 

No  one  who  is  not  thoroughly  upright  is  to  be  trusted, 

This  man  is  not  thoroughly  upright, 

Therefore  this  man  is  not  to  be  trusted. 


§30.    THE  FIGURES   OF  THE  SYLLOGISM  113 

in  this  example,  although  the  form  of  both  premises  is  negative, 
the  minor  premise  supplies  a  positive  basis  for  argument,  and  is 
really  affirmative  in  character.  Or  we  may  say  that  the  '  not '  in  the 
predicate  of  the  minor  premise  belongs  to  the  predicate,  and  not  to 
the  copula.  The  proposition  may  therefore  be  said  to  affirm,  rather 
than  to  deny. 

The  seventh  and  eighth  rules,  which  refer  to  particular  premises, 
can  be  proved  by  considering  separately  all  the  possible  cases.  If 
this  is  done,  it  will  be  found  that  these  rules  are  direct  corollaries 
from  the  third  and  fourth,  which  are  concerned  with  the  proper  dis- 
tribution of  terms.  It  is  impossible  to  secure  the  necessary  distri- 
bution with  two  particular  premises ;  for  either  the  distribution  of 
the  middle  term  will  not  be  provided  for.  or  if  this  has  been  secured 
by  means  of  a  negative  premise,  the  conclusion  will  show  a  case  of 
the  illicit  major  term.  By  means  of  the  same  rules,  it  may  be 
shown  that  a  particular  premise  always  requires  a  particular  con- 
clusion. The  truth  of  these  two  subordinate  canons  may  be  also 
readily  shown  by  the  use  of  circles. 

§  30.  The  Figures  of  the  Syllogism,  —  We  have  seen 
what  an  important  part  the  middle  term  plays  in  the 
syllogism.  It  constitutes  the  mediating  link  between 
the  major  and  minor  terms,  and  makes  possible  their 
union.  Now  upon  the  position  of  the  middle  term  in  the 
premises  depends  the  Figure  of  the  syllogism.  There 
are  four  possible  arrangements  of  the  middle  term  in 
the  two  premises,  and  therefore  four  figures  of  the 
syllogism.  If  we  let  P  represent  the  major  term,  S  the* 
minor,  and  M  the  middle  term,  the  form  of  the  different 
figures  may  be  represented  as  follows  :  — 

FIRST  FIGURE  SECOND  FIGURE 

M— P  P— M 

S  — M  S  — M 


.-.  S  — P  .-.  S  — P 

i 


114  THE  SYLLOGISM 

THIRD  FIGURE  FOURTH  FIGURE 

M  —  P  P  —  M 

M  —  S  M  —  S 


.-.  S  —  P  .-.  S  —  P 

In  the  first  figure,  the  middle  term  is  the  subject  of 
the  major  premise,  and  the  predicate  of  the  minor 
premise. 

In  the  second  figure,  the  middle  term  is  predicate  of 
both  major  and  minor  premises. 

The  third  figure  has  the  middle  term  as  the  subject 
of  both  premises. 

In  the  fourth  figure,  the  middle  term  occupies  just  the 
opposite  position  in  the  two  premises  from  that  which 
it  held  in  the  first  figure ;  i.e.,  it  is  the  predicate  of  the 
major  premise,  and  the  subject  of  the  minor  premise. 


CHAPTER   IX 

THE    VALID    MOODS    AND    THE    REDUCTION    OF    FIGURES 

§  31.   The  Moods  of  the  Syllogism.  —  By  the  Mood  of 

a  syllogism  we  mean  the  combination  of  propositions 
A,  E,  I,  and  O,  which  goes  to  make  it  up.  Thus,  when 
a  syllogism  is  made  up  of  three  universal  affirmative 
propositions,  we  speak  of  it  as  the  mood  AAA ;  if  it 
is  composed  of  a  universal  negative,  a  particular  affirma- 
tive, and  a  particular  negative  proposition,  we  name  it 
the  mood  EIO. 

Every  syllogism,  as  has  been  already  stated,  is  made 
up  of  some  arrangement  of  the  four  propositions 
A,  E,  I,  O,  taken  three  at  a  time.  Now,  there  are  in 
all  sixty-four  possible  permutations  of  these  four  propo- 
sitions taken  three  at  a  time.  We  might  then  write 
out  these  sixty-four  moods,  and  proceed  to  determine 
which  of  them  are  valid.  But  this  would  be  a  long  and 
somewhat  tedious  undertaking.  Moreover,  if  we  can 
determine  what  are  the  valid  premises,  we  can  draw  the 
proper  conclusions  for  ourselves.  Since,  then,  there 
are  but  two  premises  in  each  syllogism,  we  shall  have  to 
deal  only  with  the  possible  permutations  of  A,  E,  I,  and  O, 
taken  two  at  a  time,  or  with  sixteen  combinations  in  all. 

The  following,  then,  are  the  only  possible  ways  in 
which  the  propositions  A,  E,  I,  and  O  can  be  arranged 
as  premises ;  — 


Il6     VALID   MOODS   AND  THE   REDUCTION   OF   FIGURES 


AA 

EA 

IA 

OA 

AE 

EE 

IE 

OE 

AI 

El 

II 

01 

AO 

EO 

10 

00 

Some  of  these  premises,  however,  cannot  yield  conclu- 
sions, since  they  plainly  violate  certain  rules  of  the  syllo- 
gism. The  combinations  of  negative  premises  EE, 
EO,  OE,  and  OO  can  be  at  once  struck  out.  Again, 
since  no  conclusion  follows  from  two  particular  prem- 
ises, we  can  eliminate  II,  IO,  and  OI.  There  remain, 
then,  for  further  consideration  the  combinations  :  — 

AA  EA  IA  OA 

AE  IE 

AI  El 

AO 

At  this  point  we  must  recall  the  fact  that  every 
argument  must  belong  to  one  of  the  four  figures.  We 
must  now  therefore  ask  this  question :  Which  of  the 
above  combinations  of  premises  will  yield  valid  con- 
clusions in  the  first,  second,  third,  and  fourth  figures, 
respectively  ?  By  examining  the  form  of  the  syllogism 
in  each  of  these  figures,  we  shall  be  able  to  discover 
what  conditions  must  be  fulfilled  in  each  case,  and 
to  lay  down  special  canons  for  each  figure.  We  shall 
first  proceed  to  state  and  prove  the  special  canons  of 
the  different  figures.  It  will  not,  however,  be  necessary 
for  the  student  to  commit  these  rules  to  memory,  as  he 
can  always  derive  them  for  himself  by  a  consideration 
of  the  form  of  the  argument  in  the  different  figures, 


§32.    THE   SPECIAL   CANONS   OF  THE   FOUR   FIGURES     1 17 

§  32.  The  Special  Canons  of  the  Four  Figures.  —  In  the 
first  figure,  tJie  minor  premise  must  be  affirmative,  and 
the  major  premise  universal. 

The  first  figure  is  of  the  form :  — 

M  -  -  P 

S  —  M 


.-.  S  —  P 

To  show  that  the  minor  premise  is  affirmative,  we 
employ  the  indirect  method  of  proof.  Let  us  suppose 
that  the  minor  premise  is  not  affirmative,  but  negative. 
Then  since  one  premise  is  negative,  the  conclusion  must 
be  negative.  But  if  the  conclusion  is  a  negative  propo- 
sition, its  predicate,  P,  must  be  distributed.  Any  term 
which  is  distributed  in  the  conclusion  must,  however, 
have  been  distributed  when  it  was  used  in  the  premise. 
P  must  be  distributed,  therefore,  as  the  predicate  of  the 
major  premise.  But  since  negatiye^propasitions  alone 
distribute  their  predicates,  the  major  premise,  M  —  P, 
must  be  negative.  But  by  hypothesis  the  minor  prem- 
ise, S  —  M,  is  negative.  We  have,  therefore,  two 
negative  premises,  which  is  impossible.  Our  suppo- 
sition, that  the  minor  premise  is  negative,  is  therefore 
false ;  or,  in  other  words,  the  minor  premise  must  be 
affirmative. 

This  having  been  established,  we  can  very  easily 
prove  that  the  major  premise  must  be  universal.  For 
the  middle  term,  M,  must  be  distributed  in  at  least  one 
of  the  premises.  But  it  is  not  distributed  in  the  minor 
premise,  for  it  is  there  the  predicate  of  an  affirmative 
proposition.  It  must,  therefore,  be  distributed  as  the 


Il8    VALID   MOODS  AND  THE  REDUCTION   OF  FIGURES 

subject  of  the  major  premise,  that  is,  the  major  premise 
must  be  universal. 

If  we  turn  now  to  the  second  figure,  we  shall  find 
that  the  following  rules  may  be  deduced  from  a  con- 
sideration of  its  form  :  — 

(1)  One  premise  must  be  negative,  and  the  conclusion 
therefore  negative. 

(2)  The  major  premise  must  be  universal. 
The  second  figure  is  in  the  form :  — 

P  —  M 
S  —  M 


.-.  S  —  P 

The  reason  for  the  first  rule  is  at  once  evident.  If  one 
premise  is  not  negative,  the  middle  term,  M,  is  not 
distributed,  and  no  conclusion  is  therefore  possible. 
The  only  means  of  securing  distribution  of  the  middle 
term  in  the  second  figure  is  by  means  of  a  negative 
premise.  And  if  one  premise  is  negative,  it  of  course 
follows  that  the  conclusion  must  be  negative. 

This  having  been  established,  the  proof  of  rule  2 
follows  almost  immediately.  For,  since  the  conclusion 
is  negative,  its  predicate,  P,  must  be  distributed.  And 
since  P  is  distributed  in  the  conclusion,  it  must  have 
been  used  distributively  when  it  occurred  as  the  subject 
of  the  major  premise,  or,  in  other  words,  the  major 
premise  must  be  universal. 

The  third  figure  is  of  the  form  :  — 
M  —  P 
M  —  S 

.-.    S  —  P 


§32.    THE  SPECIAL  CANONS   OF   THE   FOUR  FIGURES     119 

From  an  analysis  of  this,  the  two  following  rules  may 
be  obtained :  — 

(1)  The  minor  premise  must  be  affirmative. 

(2)  The  conclusion  must  be  particular. 

The  minor  premise  is  here  shown  to  be  affirmative 
by  the  method  employed  in  proving  the  same  rule  in 
the  first  figure.  That  is,  we  suppose  the  minor  premise 
negative,  and  show  that,  as  a  result  of  this  hypothesis, 
the  conclusion  is  negative,  and  the  major  term  dis- 
tributed. It  follows,  then,  that  this  term  must  be  dis- 
tributed as  the  predicate  of  the  major  premise.  But 
this  could  happen  only  if  this  premise  were  negative. 
The  hypothesis  that  the  minor  premise  is  negative  thus 
leads  to  the  absurdity  of  two  negative  premises.  The 
conclusion  that  the  opposite  is  true,  that  the  minor 
premise  is  affirmative,  is  therefore  proved  indirectly. 

Since  the  minor  premise  is  affirmative,  its  predicate 
S  is  undistributed.  This  term  must  therefore  be  used 
in  an  undistributed,  i.e.y  particular  sense  in  the  conclu- 
sion. And,  as  this  term  forms  its  subject,  the  conclu- 
sion is  particular. 

In  the  fourth  figure  the  terms  are  arranged  in  the 

following  way  :  — • 

P  —  M 
M  —  S 


.-.  S  —  P 


From  a  consideration  of  the  form  of  this  figure  we  can 
obtain  the  following  special  canons  :  — 

(i)  If  either  premise  be  negative,  the  major  premise 
must  be  universal. 


120     VALID   MOODS  AND  THE   REDUCTION  OF  FIGURES 

(2)  If  the  major  premise  be  affirmative ',  the  minor  must 
be  universal. 

(3)  If  the  minor  premise  be  affirmative,  the  conclusion 
must  be  particular. 

The  student  will  be  able  to  prove  these  canons  for 
himself  by  applying  the  rules  of  the  syllogism  in  the 
same  way  as  has  been  done  in  the  proofs  already  given. 

§  33.  The  Determination  of  the  Valid  Moods  in  Each  of 
the  Figures. — We  have  now  to  apply  these  special 
canons  in  order  to  determine  what  moods  are  valid  in 
each  of  the  four  figures.  It  has  already  been  shown 
(p.  1 1 6)  that  the  premises  which  are  not  excluded  by 
the  general  rules  of  the  syllogism  are :  — 

AA  EA  IA  OA 

AE  IE 

AI  El 

AO 

Now  we  have  proved  that  in  the  first  figure  the  major 
premise  must  be  universal,  and  the  minor  affirmative. 
The  only  combinations  of  premises  which  will  stand 
these  tests  are,  AA,  EA,  AI,  and  El.  Drawing  the 
proper  conclusion  in  each  case,  we  have  as  the  four 
valid  moods  of  the  first  figure :  — 

AAA,  EAE,  All,  EIO. 

It  will  be  noticed  that  the  first  figure  enables  us  to 
obtain  as  conclusion  any  one  of  the  four  logical  propo- 
sitions, A,  E,  I,  and  O. 

The  special  canons  of  the  second  figure  state  that 


§  33-    THE  DETERMINATION  OF  THE  VALID   MOODS     1 2 1 

the  major  premise  must  be  universal,  and  one  premise 
negative.  Selecting  the  combinations  of  premises 
which  fulfil  these  conditions,  we  obtain  EA,  AE,  El, 
and  AO.  These  give,  when  the  conclusions  have  been 
drawn,  the  following  four  moods  of  the  second  figure  :  — 

EAE,  AEE,  EIO,  AGO. 

By  means  of  the  second  figure,  therefore,  we  are  able 
to  establish  the  truth  only  of  the  negative  propositions, 
E  and  O. 

In  the  third  figure  the  minor  premise  must  be  affirma- 
tive, and  the  conclusion  particular.  Taking  all  the 
combinations  in  which  the  minor  is  affirmative,  there 
result,  AA,  IA,  AI,  EA,  OA,  EL  It  must  be  remem- 
bered that  the  third  figure  yields  only  particular  con- 
clusions, even  where  both  premises  are  universal.  The 
valid  moods  in  this  figure  are  therefore  as  follows  :  — 

AAI,  IAI,  AH,  EAO,  OAO,  EIO. 

The  canons  of  the  fourth  figure,  which  have  to  do 
with  the  premises,  state  that  where  either  premise  is 
negative,  a  universal  major  is  necessary,  and  that  an 
affirmative  major  premise  must  be  accompanied  by  a 
universal  minor.  The  combinations  of  propositions 
which  fulfil  these  conditions  are  AA,  AE,  IA,  EA, 
and  EL  In  drawing  conclusions  from  these  premises, 
however,  it  is  necessary  to  pay  attention  to  the  third 
canon  of  this  figure,  which  states  that  where  the  minor 
premise  is  affirmative,  the  conclusion  must  be  particular. 
Accordingly,  the  valid  moods  of  this  figure  may  now 
be  written :  — 


122     VALID   MOODS  AND  THE   REDUCTION   OF  FIGURES 

AAI,  AEE,  IAI,  EAO,  EIO. 

Here  we  are  able  to  obtain  a  universal  negative  as  a 
conclusion,  but  not  a  universal  affirmative.  It  is  inter- 
esting to  notice  that  the  first  figure  alone  enables  us 
to  prove  a  proposition  of  the  form  A. 

It  may  also  be  pointed  out  that  the  combination  IE, 
although  not  excluded  by  the  general  rules  of  the  syl- 
logism, cannot  be  used  at  all  as  premises,  since  it  vio- 
lates the  canons  of  all  four  figures.  There  remain  in 
all,  then,  nineteen  valid  moods  of  the  syllogism,  —  four 
in  the  first  figure,  four  in  the  second,  six  in  the  third, 
and  five  in  the  fourth  figure. 

§  34.  The  Mnemonic  Lines.  —  It  is  not  necessary  to 
commit  to  memory  the  valid  moods  in  each  figure.  By 
applying  the  general  rules  of  the  syllogism  to  the  figure 
in  question,  the  student  will  be  able  to  determine  for 
himself  in  every  case  whether  or  not  an  argument  is 
valid.  The  Latin  Schoolmen  in  the  thirteenth  century, 
however,  invented  a  system  of  curious  mnemonic  verses 
for  the  purpose  of  rendering  it  easy  to  remember  the 
valid  moods  in  each  figure.  Although  it  is  not  neces- 
sary for  the  student  to  burden  his  memory  with  these 
barbarous  names,  it  is  interesting  to  understand  the  use 
of  the  lines  :  — 

Barbara,  CeZarent,  Darti,  ttrt'oque  prioris  ; 
Cesar e,  Camestres,  Festino,  Baroko,  secundae ; 
Tertia,  Darapti,  Disamis,  Datisi,  Felapton, 
Bokardo,  Ferison,  habet ;  Quarta  insuper  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison. 

The  words   printed   in   ordinary  type   are   real   Latin 


§  34-    THE   MNEMONIC   LINES  123 

words,  indicating  that  the  four  moods  represented  by 
Barbara,  Celarent,  Darii,  and  Ferio  are  the  valid  moods 
of  the  first  figure,  that  the  next  four  are  valid  in  the 
second  figure,  that  the  third  figure  has  six  valid  moods 
represented  by  as  many  artificial  names,  and  that  the 
fourth  figure  adds  five  more.  Each  word  represents  a 
mood,  the  vowels  A,  E,  I,  and  O  indicating  the  quality 
and  quantity  of  the  propositions  which  go  to  compose 
them.  Thus,  Barbara  signifies  the  mood  of  the  first 
figure  which  is  made  up  of  three  universal  affirmative 
propositions  A  A  A;  Cesare,  a  mood  of  the  second 
figure,  composed  of  the  three  .propositions  E  A  E. 
These  lines,  then,  sum  up  the  results  reached  on 
pages  1 20-22  regarding  the  valid  moods  in  each  figure. 
But  certain  consonants  in  these  mnemonic  words  also 
indicate  how  arguments  in  the  second,  third,  or  fourth 
figures  may  be  changed  to  the  form  of  the  first  figure. 
The  first  figure  was  called  by  Aristotle  the  perfect 
figure,  and  the  second  and  third  the  imperfect  figures, 
since  he  did  not  regard  an  argument  in  these  forms  as 
so  direct  and  convincing  as  one  of  the  first-mentioned 
type.  The  fourth  figure  was  not  recognized  by  Aris- 
totle, but  is  said  to  have  been  introduced  into  logic  by 
Galen,  the  celebrated  teacher  of  medicine,  who  lived  in 
the  latter  half  of  the  second  century.  The  process  of 
changing  an  argument  from  one  of  the  so-called  imper- 
fect figures  to  that  of  the  first  figure  is  known  as  Reduc- 
tion. And,  as  we  have  said,  these  curious  but  ingenious 
mnemonic  words  give  rules  for  carrying  out  this  process. 
For  example,  s  indicates  that  the  proposition  represented 
by  the  preceding  vowel  is  to  be  converted  simply.  Thus 


124    VALID   MOODS  AND  THE   REDUCTION  OF   FIGURES 

an  argument  in  the  second  figure  of  the  mood  Cesare 
is  changed  to  Celarent  in  the  first  figure,  by  converting 
the  major  premise  simply.  Again,  /  denotes  that  the 
preceding  vowel  is  to  be  converted  by  limitation,  or  per 
accidens ;  m  is  supposed  to  stand  for  mutare,  and  indi- 
cates that  the  premises  are  to  be  transposed ;  /-,  which 
is  used  in  the  moods  Baroko  and  Bokardo,  shows  that 
an  indirect  method  of  proof  or  reduction  is  necessary 
to  reduce  the  arguments  to  the  first  figure. 

Further,  the  initial  consonants  of  the  moods  of  the  im- 
perfect figures  correspond  with  those  of  the  moods  in  the 
first  figures,  to  which  they  can  be  reduced.  Cesare  and 
Camestres  of  the  second  figure,  for  example,  and  Ca- 
menes  of  the  fourth  are  reducible  to  Celarent ;  and, 
similarly,  Festino,  Felapton,  Fesapo,  and  Fresison  may 
all  be  reduced  to  Ferio. 

The  student  who  understands  the  structure  of  the  syllogism  will 
be  able  to  arrange  an  argument  in  one  figure  or  another,  as  may  be 
most  convenient,  without  the  aid  of  any  mechanical  rules.  It  may 
be  interesting,  however,  to  give  a  single  example  for  the  sake  of 
illustrating  the  workings  of  this  most  ingenious  device.  Let  us  take 
the  following  argument  in  the  second  figure  of  the  mood  AEE,  or 
Camestres :  — 

All  members  of  the  class  are  prepared  for  the  examination, 
No  idle  persons  are  prepared  for  the  examination, 

Therefore  no  idle  persons  are  members  of  the  class. 

Now  the  m  in  Camestres  shows  that  the  major  and  minor  premises 
are  to  be  transposed ;  the  first  s  indicates  that  the  minor  premise  is 
to  be  converted,  and  the  second  that  the  same  process  must  be  per- 
formed on  the  conclusion. 

Converting  the  minor  premise  and  transposing,  we  obtain  :  — 


§34-     THE   MNEMONIC   LINES  12$ 

No  persons  prepared  for  the  examination  are  idle, 
All  members  of  the  class  are  prepared  for  the  examination, 
Converting  the  conclusion, 

Therefore  no  members  of  the  class  are  idle  persons. 
This  result,  as  will  at  once  be  seen,  is  an  argument  in  the  first 
figure  of  the  mood  EAE,  or  Celarent. 

References 

Sir  W.  Hamilton,  Lectures  on  Logic.     Lectures  XX.,  XXI. 
A.  Bain,  Logic,  Part  First,  Deduction,  Bk.  II.  Ch.  I. 

NOTE.  —  It  would  be  interesting  to  work  out,  in  connection  with 
the  various  forms  of  Inductive  reasoning  treated  in  Part  II.,  the 
organic  relation  of  the  syllogistic  Figures,  and  their  natural  applica- 
bility to  various  purposes  of  argument.  This  task,  however,  seemed 
to  lie  beyond  the  proper  limits  of  this  book.  All  of  the  investiga- 
tions on  this  point  start  from  Hegel's  treatment  in  the  second  part 
of  the  Wissenschaft  der  Logik  (Werke,  Bd.  5,  pp.  115  ff.).  Those 
interested  in  this  subject  may  consult  W.  T.  Harris,  The  Psychologic 
Foundations  of  Education,  Ch.  IX. -XL,  and  the  same  author's 
Logic  of  Hegel.  See  also  B.  Bosanquet,  Logic,  Vol.  II.,  pp.  44  ff., 
88  ff.,  and  The  Essentials  of  Logic,  Lecture  X. 


CHAPTER   X 

ABBREVIATED    AND    IRREGULAR    FORMS    OF    ARGUMENT 

§35.  Enthymemes.  —  The  term  '  enthy meme '  seems  to 
have  been  used  by  Aristotle  for  an  argument  from 
signs  or  from  likelihood,  without  complete  proof. 
From  this  sense  of  logical  incompleteness,  the  name 
has  come  to  be  applied  in  modern  times  to  an  argument 
in  which  some  part  is  omitted.  We  have  already 
noticed,  in  dealing  with  the  syllogism  (§  10),  that  one 
premise  is  often  omitted.  Indeed,  it  is  but  seldom  in 
ordinary  reasoning  that  we  arrange  our  arguments  in 
the  strict  syllogistic  form.  We  hurry  on  from  one  fact 
to  another  in  our  thinking  without  stopping  to  make  all 
the  steps  definite  and  explicit.  We  feel  it  to  be  a  waste 
of  time,  and  a  trial  to  the  patience,  to  express  what  is 
clearly  obvious,  and  so  we  press  on  to  the  conclusion 
which  is,  for  the  time  being,  the  central  point  of  in- 
terest. 

But  the  more  rapid  and  abbreviated  the  reasoning, 
the  more  necessary  is  it  to  keep  a  clear  head,  and  to 
understand  what  conclusion  is  aimed  at,  and  what 
premises  are  assumed  in  the  argument.  To  bring  to 
light  the  hidden  assumption  upon  which  an  argument  is 
based,  is  often  the  best  means  of  refuting  it. 

126 


§36.     EPISYLLOGISMS  AND   PROSYLLOGISMS         127 

Enthymemes  are  sometimes  said  to  be  of  the  first, 
second,  or  third  order,  according  as  the  major  premise, 
the  minor  premise,  or  the  conclusion  is  wanting.  As  a 
matter  of  fact,  an  enthymeme  of  the  third  order  is  a 
rhetorical  device  used  to  call  special  attention  to  a  con- 
clusion which  is  perfectly  obvious,  although  suppressed. 
Thus,  for  example,  'all  boasters  are  cowards,  and  we 
have  had  proofs  that  A  is  a  boaster.'  Here  the  con- 
clusion is  at  once  obvious,  and  is  even  more  prominent 
than  if  it  were  actually  expressed. 

It  is  usually  easy  to  complete  an  enthymeme.  If  the 
conclusion  and  one  premise  are  given,  the  three  terms 
of  the  syllogism  are  already  expressed.  For  the  con- 
clusion contains  the  major  term  and  the  minor  term; 
and  one  of  these  again,  in  combination  with  the  middle 
term,  is  found  in  the  given  premise.  From  these  data, 
then,  it  will  not  be  difficult  to  construct  the  suppressed 
premise.  When  the  premises  are  given  without  the 
conclusion,  there  is  no  way  of  determining,  except  from 
the  order,  which  is  major  and  which  is  minor.  It  is 
therefore  necessary  to  assume  that  they  are  already 
arranged  in  proper  logical  order,  and  that  the  subject 
of  the  conclusion,  or  minor  term,  is  to  be  found  in  the 
second  premise,  and  the  predicate  of  the  conclusion,  or 
major  term, in  the  first  premise. 

§  36.  Prosyllogisms  and  Episyllogisms.  —  In  deductive 
reasoning  it  is  often  necessary  to  carry  on  the  argument 
through  several  syllogisms,  using  the  conclusion  first 
reached  as  a  premise  in  the  following  syllogism.  For 
example,  we  may  argue  :  — 


128  FORMS  OF  ARGUMENT 

All  B  is  A 
All  C  is  B 


.-.  All  C  is  A. 
But  all  D  is  C 

.-.  All  D  is  A. 

It  is  clear  that  we  have  here  two  arguments  in  the  first 
figure.  The  first  is  called  the  Prosyllogism,  and  the 
latter  the  Episyllogism.  If  the  argument  were  carried 
on  further,  so  as  to  include  three  or  more  syllogisms,  the 
second  would  form  the  Prosyllogism  with  respect  to 
the  third,  while  the  third  would  be  the  Episyllogism  of 
the  second.  A  concrete  example  of  this  kind  of  reason- 
ing may  now  be  given  :  — 

All  timid  men  are  suspicious, 
All  superstitious  men  are  timid, 

Therefore  all  superstitious  men  are  suspicious. 
But  some  educated  men  are  superstitious, 

Therefore  some  educated  men  are  suspicious. 

It  will  be  noticed  that  in  these  examples  the  argument  advances 
from  the  premises  of  the  Prosyllogism,  to  the  conclusion  of  the 
Episyllogism.  It  proceeds,  that  is  to  say,  in  a  forward  direction, 
developing  the  consequences  of  the  premises  which  form  its  starting- 
point.  This  mode  of  investigation  is  therefore  called  the  Progres- 
sive or  Synthetic,  since  it  goes  steadily  forward  building  up  its  results 
as  it  advances.  To  state  the  same  thing  in  different  words,  we  may 
say  that  the  Progressive  or  Synthetic  method  advances  from  the 
conditions  to  what  is  conditioned,  from  causes  to  effects. 

But  it  is  often  necessary  to  proceed  in  the  opposite  way.  We 
have  often  to  go  back  and  show  the  grounds  upon  which  our  prem- 
ises rest,  instead  of  going  forward  to  show  what  consequences 
follow  from  them.  And  when  we  do  this  we  proceed  Regressively 
or  Analytically.  To  take  an  example  which  will  illustrate  both 
ways  of  proceeding :  — 


§  37-     SORITES,   OR  CHAINS   OF   REASONING         1  29 

No  man  is  infallible,  for  no  man  is  omniscient, 
Aristotle  was  a  man, 

Therefore  Aristotle  was  not  infallible. 

In  advancing  from  the  premises  to  the  conclusion  in  this  argument 
our  procedure  is  progressive  or  synthetic.  Instead  of  reasoning  out 
the  consequences  of  the  premises,  however,  we  may  go  back  and 
show  the  grounds  upon  which  the  major  premise  rests.  It  is  evident 
that  this  premise  is  itself  the  conclusion  of  a  syllogism  which  may 
be  expressed  as  follows  :  — 

All  infallible  beings  are  omniscient, 

No  man  is  omniscient, 


Therefore  no  man  is  infallible. 
The  regressive  method  goes  backward  from  conclusions  to  premises, 
or  from  the  conditioned  to  its  necessary  conditions.  In  scientific 
investigation  it  reasons  from  effects  to  causes,  while  the  synthetic 
method  advances  from  causes  to  effects. 

§  37.  Sorites,  or  Chains  of  Reasoning.  —  A  Sorites  is 
an  abbreviated  form  of  syllogistic  reasoning  in  which 
a  subject  and  predicate  are  united  by  means  of  several 
intermediate  terms.  Such  a  train  of  reasoning  repre- 
sents several  acts  of  comparison,  and  therefore  several 
syllogistic  steps.  But  instead  of  stopping  to  draw  the 
conclusion  at  each  stage,  the  sorites  continues  the 
processes  of  comparison,  and  only  sums  up  its  results 
at  the  close.  We  may  define  the  sorites,  therefore,  as 
a  series  of  prosyllogisms  and  episyllogisms  in  which  all 
of  the  conclusions,  except  the  last,  are  suppressed.  It 
is  usually  stated  in  the  following  form  :  — 

All  A  is  B 

All  B  is  C 
»          All  C  is  D 

All  D  is  E 
.-.     All  A  is  E. 


130  FORMS  OF  ARGUMENT 

It  is  evident  that  this  train  of  reasoning  fully  expressed 
is  equivalent  to  the  following  three  syllogisms  :  - — 

FIRST  SYLLOGISM  SECOND  SYLLOGISM  THIRD  SYLLOGISM 

All  B  is  C  All  C  is  D  All  D  is  E 

All  A  is  B  All  A  is  C   (i)  All  A  is  D  (2) 


.-.  All  A  is  C  (i).        .-.  All  A  is  D  (2).      .-.  All  A  is  E  (3). 

There  are  two  rules  to  be  observed  in  using  this  form 
of  the  sorites  :  (i )  The  first  premise  may  be  particular,  all 
the  others  must  be  universal ;  (2)  the  last  premise  may 
be  negative,  all  the  others  must  be  affirmative.  It  is 
evident  from  an  examination  of  the  syllogisms  given 
above  that  if  any  premise  except  the  first  were  partic- 
ular, the  fallacy  of  undistributed  middle  would  be  com- 
mitted. For,  in  that  case,  the  middle  term  in  one  of  the 
syllogisms  would  be  the  subject  of  a  particular  propo- 
sition, and  the  predicate  of  an  affirmative  proposition. 
And  if  any  premise  but  the  last  were  negative,  the 
major  term  in  the  syllogism  following  that  in  which  this 
occurred  would  be  disturbed  in  the  conclusion  without 
having  been  distributed  in  the  major  premise.  We 
may  now  give  some  concrete  examples  of  this  kind  of 
reasoning :  — 

Misfortunes  sometimes  are  circumstances  tending  to  improve 
the  character, 

Circumstances  tending  to  improve  the  character  are  promoters 
of  happiness, 

What  promotes  happiness  is  good, 

Therefore  misfortunes  are  sometimes  good. 

In  some  cases  the  different  terms  of  an  argument  of 
this   kind   are  expressed  in  the  form  of   hypothetical 


§37-     SORITES,  OR  CHAINS  OF  REASONING          131 

propositions.  Thus,  for  example,  we  might  argue :  If 
a  man  is  avaricious,  he  desires  more  than  he  possesses ; 
if  he  desires  more  than  he  possesses,  he  is  discontented ; 
if  he  is  discontented,  he  is  unhappy ;  therefore  if  a  man 
is  avaricious,  he  is  unhappy.  This  argument  is  hypo- 
thetical in  form  only,  and  may  be  easily  reduced  to 
categorical  type  as  follows  :  — 

An  avaricious  man  is  one  who  desires  more  than  he  possesses, 
A  man  who  desires  more  than  he  possesses  is  discontented, 
A  discontented  man  is  unhappy, 
Therefore  an  avaricious  man  is  unhappy. 

It  will  be  noticed  that  the  subject  of  the  first  premise 
in  this  form  of  argument  is  taken  as  the  subject  of  the 
conclusion,  and  that  the  predicate  of  the  conclusion  is 
the  predicate  of  the  last  premise.  This  is  usually  called 
the  Aristotelian  sorites.  But  there  is  another  form 
which  unites  in  the  conclusion  the  subject  of  the  last 
premise,  and  the  predicate  of  the  first,  and  which  is 
known  as  the  Goclenian  sorites.1  This  may  be  thus 
represented :  — 

All  A  is  B 

All  C  is  A 

All  D  is  C 

All  E  is  D 


.-.  All  E  is  B. 

Since  B  is  the  predicate  of  the  conclusion,  the  prem- 
ise in  which  it  appears  is  always  to  be  regarded  as  the 
major.  As  a  result  of  this,  it  is  to  be  noticed  that  the 

1  Rudolf  Goclenius  (1547-1628),  Professor  at  Marburg,  first  explained 
this  form  in  his  Isagoge  in  Organum  Aristotlis,  1598. 


132  FORMS   OF  ARGUMENT 

suppressed  conclusions  in  this  argument  form  the  major 
premise  of  the  following  syllogism,  instead  of  the  minor 
premise  as  in  the  Aristotelian  sorites.  We  may,  there- 
fore, expand  the  reasoning  into  the  three  following 
syllogisms :  — 


FIRST  SYLLOGISM 
All  A  is  B 
All  C  is  A 

SECOND  SYLLOGISM 
All  C  is  B 
All  D  is  C 

THIRD  SYLLOGISM 
All  D  is   B 
All  E  is  D 

.'.   All  C  is  B.  .'.^All  D  is  B.  .'.  All  E  is  B. 

A  little  consideration  of  the  form  of  these  syllogisms 
will  lead  the  student  to  see  that  the  rules  given  for  the 
Aristotelian  sorites  must  be  here  reversed.  In  both 
forms  of  the  sorites  there  cannot  be  more  than  one 
negative  premise,  nor  more  than  one  particular  premise. 
In  the  Aristotelian  form,  no  premise  except  the  last  can 
be  negative,  and  no  premise  except  the  first  particular. 
In  the  Goclenian  sorites,  on  the  other  hand,  the  single 
premise  which  can  be  negative  is  the  first,  and  it  is  the 
last  alone  which  may  be  particular. 

§  38.  Irregular  Arguments.  —  There  are  a  large  num- 
ber of  arguments  employed  in  everyday  life  which  are 
valid  and  convincing,  and  yet  which  cannot  be  reduced 
to  the  syllogistic  form.  The  difficulty  with  these  argu- 
ments is  that  they  appear  to  have  four  terms,  at  least  in 
the  form  in  which  they  are  most  naturally  stated.  We 
may  discuss  such  irregular  forms  of  reasoning  under 
two  headings :  (i)  Arguments  which  deal  with  the 
relations  of  things  in  time  and  space,  or  with  their 
quantitative  determinations;  (2)  arguments  which  are 


§38.     IRREGULAR  ARGUMENTS  133 

largely  verbal  in  character,  and  may  be  said  to  depend 
upon  the  principle  of  substitution. 

(i)  As  an  example  of  the  first  class  of  argument  we 
may  take  the  following  :  — 

A  is  greater  than  B, 
B  is  greater  than  C, 


Therefore  A  is  still  greater  than  C. 

It  is  obvious  that,  although  we  have  here  four  terms, 
the  conclusion  is  valid,  and  the  form  of  argument  per- 
fectly convincing.  The  truth  seems  to  be  that  in  rea- 
soning about  quantities  we  do  not  proceed  upon  the 
syllogistic  principle  of  the  inclusion  and  exclusion  of 
terms.  But  knowing  the  continuous  nature  of  quantity, 
we  take  as  our  principle  that,  '  what  is  greater  than  that 
which  is  greater  than  another  is  a  fortiori  greater  than 
that  other.'  It  would  not,  however,  make  the  matter 
any  clearer  to  write  this  as  our  major  premise,  and 
bring  the  real  argument  under  it  in  this  way  :  — 

What  is  greater  than   that  which   is   greater  than  another  is 
still  greater  than  that  other, 

A  is  that  which  is  greater  than  that  which  is  greater  than  C, 

Therefore  A  is  still  greater  than  C. 

What  we  have  here  given  as  the  major  premise  is 
simply  a  statement  of  the  nature  of  quantity,  not  a 
premise  from  which  the  conclusion  is  derived.  We  find 
the  same  irregularity  in  arguments  referring  to  the  rela- 
tions of  things  in  space  and  time :  — 

A  is  situated  to  the  east  of  B, 
B  is  situated  to  the  east  of  C, 

Therefore  A  is  to  the  east  of  C. 


134  FORMS  OF  ARGUMENT 

In  spite  of  the  formal  deficiency  of  four  terms  the 
argument  is  valid.  It  will  be  observed,  too,  that  it  is 
in  virtue  of  the  comparison  of  the  position  of  A  and 
of  C  with  that  of  B,  that  these  relative  positions  have 
been  determined.  The  principle  upon  which  we  pro- 
ceed may  be  said  to  be  that,  '  what  is  to  the  east  of  B 
is  to  the  east  of  that  which  B  is  to  the  east  of.'  Or 
perhaps  it  would  be  truer  to  fact  to  say  that  we  proceed 
in  such  cases  upon  what  we  know  regarding  the  nature 
of  space,  and  the  relations  of  objects  in  space. 

(2)  The  second  class  of  irregular  arguments  are 
largely  verbal  in  character,  and  may  be  dealt  with  very 
briefly.  As  an  example  we  may  consider :  — 

Men  are  willing  to  risk  their  lives  for  gold, 
Gold  cannot  buy  happiness, 

Therefore  men  are  willing  to  risk  their  lives  for  what  cannot  buy 
happiness. 

It  is  doubtful,  I  think,  whether  these  propositions  rep- 
resent any  real  inference.  The  whole  process  may 
be  regarded  as  a  verbal  substitution  in  the  major  prem- 
ise of  '  what  cannot  buy  happiness '  for  the  word  '  gold.' 
By  a  slight  change  in  the  form  of  the  proposition,  how- 
ever, the  argument  may  be  expressed  as  a  regular 
syllogism  of  the  third  figure :  — 

Gold  is  something  for  which  men  are  willing  to  risk  their  lives, 
Gold  cannot  buy  happiness, 

Therefore  something  which  cannot  buy  happiness  is  something 
for  which  men  are  willing  to  risk  their  lives. 

Another  example  which  also  appears  to  be  irregular 
at  first  sight  is  added  :  — 


§38.     IRREGULAR  ARGUMENTS  135 

The  men  of  the  Middle  Ages  were  ready  to  undertake  any  expe- 
dition where  glory  could  be  won, 

The  crusades  were  expeditions  in  which  glory  could  be  won, 

The  crusades,  therefore,  were  readily  undertaken  by  the  men  of 
the  Middle  Ages. 

This  argument  seems  to  be  irregular  in  form  only,  and 
by  a  slight  change  in  form  may  be  expressed  in  the  first 
figure :  — 

All  expeditions  in  which  glory  could  be  won  were  readily  under- 
taken by  the  men  of  the  Middle  Ages, 

The  crusades  were  expeditions  in  which  glory  could  be  won, 

Therefore  the  crusades  were  readily  undertaken  by  the  men  of 
the  Middle  Ages. 

References,  especially  for  §  38 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  p.  152. 
"     "        "        The  Principles  of  Science.  Introduction. 
F.  H.  Bradley,  The  Principles  of 'Logic -,  pp.  348-360. 


CHAPTER   XI 

HYPOTHETICAL    AND    DISJUNCTIVE    ARGUMENTS 

§  39.  The  Hypothetical  Syllogism.  — We  have  hitherto 
been  dealing  with  syllogisms  composed  entirely  of  cate- 
gorical propositions,  and  have  not  referred  to  the  use 
which  is  made  of  conditional  propositions  in  reasoning. 
A  conditional  proposition  is  sometimes  defined  as  the 
union  of  two  categorical  propositions  by  means  of  a 
conjunction.  It  is  the  expression  of  an  act  of  judg- 
ment which  does  not  directly  or  unambiguously  assert 
something  of  reality.  We  have  already  pointed  out 
(§  20)  that  there  are  two  classes  of  conditional  propo- 
sitions :  the  hypothetical  and  the  disjunctive,  and  corre- 
sponding to  these  we  have  the  hypothetical  and  the 
disjunctive  syllogism.  The  hypothetical  syllogism  has 
a  hypothetical  proposition  as  a  major  premise,  and  a 
categorical  proposition  as  a  minor  premise.  The  dis- 
junctive syllogism  in  the  same  way  is  composed  of  a 
disjunctive  proposition  as  major,  and  a  categorical 
proposition  as  minor,  premise.  In  addition  to  these, 
we  shall  have  to  treat  of  another  form  of  argument 
called  the  'dilemma,'  which  is  made  up  of  hypothetical 
and  disjunctive  propositions. 

A  hypothetical  proposition  asserts  something  not  di- 
rectly, but  subject  to  some  limitation  or  condition.  It 
is  usually  introduced  by  some  word  or  conjunctive 

136 


§39-    THE  HYPOTHETICAL  SYLLOGISM  137 

phrase,  like  'if,'  'supposing,'  or  'granted  that';  as,  e.g., 
'if  he  were  to  be  trusted,  we  might  give  him  the  mes- 
sage' ;  '  suppose  that  A  is  B,  then  C  is  D.'  The  part  of 
a  hypothetical  proposition  which  expresses  the  suppo- 
sition or  condition  is  known  as  the  Antecedent ;  the 
clause  stating  the  result  is  called  the  Consequent.  Thus, 
in  the  proposition,  '  he  would  write  if  he  were  well,'  the 
consequent,  'he  would  write,'  is  stated  first,  and  the 
antecedent,  '  if  he  were  well,'  follows. 

The  hypothetical  syllogism,  as  has  been  already  re- 
marked, has  a  hypothetical  proposition  as  its  major,  and 
a  categorical  proposition  as  its  minor,  premise  :  — 

If  justice  is  to  prevail,  his  innocence  will  be  proved, 
And  justice  will  prevail, 

Therefore  his  innocence  will  be  proved. 

It  will  be  noticed  that  in  this  argument  the  minor 
premise  affirms  the  antecedent,  and  that,  as  a  result, 
the  conclusion  affirms  the  consequent.  This  form  is 
known  as  the  constructive  hypothetical  syllogism,  or  the 
modus  ponens. 

In  the  following  example  it  will  be  observed  that  the 
conseqiient  is  denied,  and  the  conclusion  obtained  is 
therefore  negative.  . 

If  he  were  well,  he  would  write, 
He  has  not  written, 

Therefore  he  is  not  well. 

This  is  called  the  destructive  hypothetical  syllogism,  or 
modus  tollens. 

The  rule  of  the  hypothetical  syllogism  may  therefore 
be  stated  as  follows :  Either  affirm  the  antecedent  or 


138     HYPOTHETICAL  AND   DISJUNCTIVE  ARGUMENTS 

deny  the  consequent.  If  we  affirm  the  antecedent,  i.e., 
declare  that  the  condition  exists,  the  consequent  neces- 
sarily follows.  And,  on  the  other  hand,  if  the  conse- 
quent is  declared  to  be  non-existent,  we  are  justified 
in  denying  that  the  condition  is  operative. 

The  violation  of  these  rules  gives  rise  to  the  fallacies 
of  denying  the  antecedent,  and  of  affirming  the  consequent. 
Thus,  for  example,  we  might  argue  :  — 

If  he  were  well,  he  would  write, 
But  he  is  not  well, 

Therefore  he  will  not  write. 

Here  the  antecedent  is  denied,  and  the  argument  plainly 
false.  For  we  cannot  infer  that  his  being  well  is  the 
only  condition  under  which  he  would  write.  We  do 
not  know,  in  other  words,  that  the  antecedent  stated 
here  is  the  only,  or  essential  condition  of  the  conse- 
quent. We  know  that  if  there  is  fire,  there  must  be 
heat ;  but  we  cannot  infer  that  there  is  no  heat  when 
no  fire  is  present.  Of  course,  if  we  can  be  certain 
that  our  antecedent  expresses  the  essential  condition,  or 
real  sine  qua  non  of  the  consequent,  we  can  go  from 
the  denial  of  the  former  to  that  of  the  latter.  For 
example :  — 

If  a  triangle  is  equilateral,  it  is  also  equiangular, 
This  triangle  is  not  equilateral, 

Therefore  it  is  not  equiangular. 

Usually,  however,  when  the  hypothetical  form  of  ex- 
pression is  employed,  we  cannot  be  certain  that  the 
antecedent  expresses  the  sole,  or  essential  condition,  of 
the  consequent.  At  the  ordinary  stages  of  knowledge 


§4o.  CATEGORICAL  AND  HYPOTHETICAL  ARGUMENTS     139 

we  have  to  content  ourselves  with  reasoning  from  ante- 
cedent conditions,  without  being  able  to  show  that  no 
other  condition  is  possible. 

To  illustrate  the  fallacy  of  affirming  the  consequent, 
we  may  take  the  following  example  :  — 

If  perfect  justice  prevailed,  the  rich  would  not  be  permitted  to  rob 
the  poor, 

But  the  rich  are  not  permitted  to  rob  the  poor, 

Therefore  perfect  justice  prevails. 

Here  it  will  be  noticed  that  the  consequent  states  only 
one  result  of  the  prevalence  of  'perfect  justice.'  Be- 
cause the  consequent  is  declared  to  exist,  it  by  no 
means  follows  that  it  exists  as  a  consequence  of  the 
operation  of  this  condition.  It  is  also  worth  noting 
in  this  example  that  the  consequent  of  the  major  prem- 
ise is  negative.  The  minor  premise  which  affirms  the 
consequent  also  takes  a  negative  form.  To  deny  the 
consequent  we  should  have  to  say,  'the  rich  are 
permitted  to  rob  the  poor.'  Or,  to  put  the  matter  gen- 
erally, it  is  necessary  to  remember  that  the  affirmation 
of  a  negative  proposition  is  expressed  by  a  negative 
proposition,  and  that  the  denial  of  a  negative  —  the 
negation  of  a  negation  —  is,  of  course,  positive  in  form. 

§  40.  Relation  of  Categorical  and  Hypothetical  Argu- 
ments. —  It  is  evident  that  the  form  of  the  hypothetical 
syllogism  is  very  different  from  that  of  the  categorical. 
But,  although  this  is  the  case,  it  must  not  be  supposed 
that  with  the  former  we  have  passed  to  a  new  and 
wholly  distinct  type  of  reasoning.  In  hypothetical 


140    HYPOTHETICAL  AND  DISJUNCTIVE  ARGUMENTS 

reasoning,  as  in  categorical,  it  is  the  presence  of  a 
universal  principle  which  enables  us  to  bring  two  facts 
into  relation  which  formerly  stood  apart.  Indeed,  in 
many  cases,  it  is  a  matter  of  indifference  in  which  form 
the  argument  is  stated.  Thus,  we  may  argue  in  hypo- 
thetical form :  — 

If  a  man  is  industrious,  he  will  be  successful, 
A  is  an  industrious  man, 

Therefore  A  will  be  successful. 

The  same  argument  may,  however,  be  expressed  equally 
well  in  categorical  form  :  — 

All  industrious  men  will  be  successful. 
A  is  an  industrious  man, 


Therefore  A  will  be  successful. 

It  is  clear  that,  in  spite  of  the  different  forms  in  which 
the  argument  is  expressed,  the  reasoning  is  essentially 
the  same  in  both  cases.  The  middle  term,  or  general 
principle  which  makes  it  possible  to  unite  the  subject 
and  predicate  of  the  conclusion,  in  the  hypothetical  as 
well  as  in  the  categorical  syllogism,  is  'industrious.'  A 
will  be  successful,  we  argue,  because  he  is  industrious, 
and  it  is  a  rule  that  industrious  men  are  successful. 

Moreover,  if  an  argument  is  fallacious  in  one  form,  it 
will  also  be  fallacious  when  expressed  in  the  other. 
The  defects  of  an  argument  cannot  be  cured  simply 
by  a  change  in  its  form.  When  a  hypothetical  argu- 
ment, in  which  the  antecedent  is  denied,  is  expressed 
categorically,  we  have  the  fallacy  of  the  illicit  major 
term.  Thus,  to  state  the  example  of  denying  the  ante- 
cedent given  on  page  138,  we  get:  — 


§40.  CATEGORICAL  AND    HYPOTHETICAL  ARGUMENTS     14! 

The  case  of  his  being  well  is  a  case  of  his  writing, 
The  present  is  not  a  case  of  his  being  well, 

Therefore  the  present  is  not  a  case  of  his  writing. 

Similarly,  when  an  argument  in  which  the  consequent 
is  affirmed  is  changed  to  the  categorical  form,  the 
defect  in  the  reasoning  appears  as  the  fallacy  of  un- 
distributed middle :  — 

If  this  tree  were  an  oak,  it  would  have  rough  bark  and  acorns, 
This  tree  has  rough  bark  and  acorns, 

Therefore  it  is  an  oak. 

When  this  argument  is  expressed  in  categorical  form, 
it  is  at  once  clear  that  the  middle  term  is  not  distributed 
in  either  the  major  or  minor  premise :  — 

All  oak  trees  are  trees  having  rough  bark  and  acorns, 
This  tree  is  a  tree  having  rough  bark  and  acorns, 

Therefore  this  tree  is  an  oak. 

The  change  from  the  categorical  to  the  hypothetical 
form  of  argument,  then,  does  not  imply  any  essential 
change  in  the  nature  of  the  reasoning  process  itself. 
Nevertheless,  it  is  important  to  note  that  hypothetical 
propositions  and  hypothetical  arguments  emphasize  one 
aspect  of  thinking,  which  is  entirely  neglected  by  the 
theory  of  the  categorical  syllogism.  When  dealing  with 
the  extension  of  terms  (§  16),  we  pointed  out  that  every 
term,  as  actually  used  in  a  proposition,  has  both  an  ex- 
tensive and  an  intensive  function.  That  is,  the  terms  of 
a  proposition  are  employed  both  to  name  certain  objects 
or  groups  of  objects,  and  to  connote  or  imply  certain 
attributes  or  qualities.  In  the  proposition,  'these  are 
oak  trees,'  the  main  purpose  is  to  identify  the  trees 


142     HYPOTHETICAL  AND  DISJUNCTIVE  ARGUMENTS 

given  in  perception  with  the  class  of  oak  trees.  When, 
on  the  other  hand,  we  say,  '  ignorant  people  are  super- 
stitious,' the  proposition  does  not  refer  directly  to  any 
particular  individuals,  but  states  the  necessary  con- 
nection between  ignorance  and  superstition.  Although 
the  existence  of  ignorant  persons  who  are  also  super- 
stitious is  presupposed  in  the  proposition,  its  most 
prominent  function  is  to  assert  a  connection  of  at- 
tributes which  is  wholly  impersonal.  We  may  perhaps 
say  that,  in  spite  of  the  categorical  form,  the  proposition 
is  essentially  hypothetical  in  character.  Its  meaning 
might  very  well  be  expressed  by  the  statement,  'if  a  man 
is  ignorant,  he  is  also  superstitious.'  What  is  here 
emphasized  is  not  the  fact  that  ignorant  persons  exist, 
and  are  included  in  the  class  of  superstitious  persons, 
but  rather  the  general  law  of  the  necessary  connection 
of  ignorance  and  superstition.  The  existence  of  indi- 
viduals to  whom  the  law  applies  is,  of  course,  presup- 
posed by  the  proposition.  It  is  not,  however,  its  main 
purpose  to  directly  affirm  their  existence. 

We  have  reached,  then,  the  following  position : 
Every  judgment  has  two  sides,  or  operates  in  two  ways. 
On  the  one  hand,  it  asserts  the  existence  of  individual 
things,  and  sets  forth  their  qualities  and  relations  to 
other  things.  But,  at  the  same  time,  every  judgment 
seeks  to  go  beyond  the  particular  case,  and  to  read  off  a 
general  law  of  the  connection  of  attributes  or  qualities 
which  shall  be  true  universally.  In  singular  and  par- 
ticular propositions,  the  categorical  element — the  direct 
assertion  of  the  existence  of  particular  objects  —  is  most 
prominent,  although  even  here  the  hint  or  suggestion 


§40.  CATEGORICAL  AND    HYPOTHETICAL  ARGUMENTS     143 

of  a  general  law  is  not  altogether  absent.  When  we 
reach  the  universal  proposition,  however,  the  reference 
to  real  things  is  much  less  direct,  and  the  meaning 
seems  capable  of  expression  in  hypothetical  form. 

Now  in  the  chapters  on  the  categorical  syllogism 
this  latter  aspect  of  judgments  has  been  left  out  of 
account.  Propositions. were  there  interpreted  as  refer- 
ring directly  to  objects,  or  classes  of  objects  (cf.  §  23). 
The  proposition,  S  is  P,  for  example,  was  taken  to 
affirm  that  some  definite  object,  or  class  of  objects, 
S,  falls  within  the  class  P.  And  the  fact  that  it 
is  possible  to  apply  this  theory  shows  that  it  repre- 
sents one  side  of  the  truth.  But  the  student  must 
sometimes  have  felt  that,  in  this  procedure,  the  most 
important  signification  of  the  proposition  is  lost  sight 
of.  It  seems  absurd  to  say,  for  example,  that  in  the 
proposition,  'all  material  bodies  gravitate,'  the  class  of 
'material  bodies'  is  included  in  the  wider  class  of 
'things  that  gravitate.'  The  main  purpose  of  the  judg- 
ment is  evidently  to  affirm  the  necessary  connection 
of  the  attributes  of  materiality  and  gravitation.  The 
judgment  does  not  refer  directly  to  things,  or  classes  of 
things  at  all,  but  asserts  without  immediate  reference  to 
any  particular  object,  z/"  material,  then  gravitating.  The 
propositions  of  geometry  are  still  more  obviously  hypo- 
thetical in  character.  'The  three  angles  of  a  triangle 
are  equal  to  two  right  angles,'  for  example,  cannot, 
without  violence,  be  made  to  mean  that  the  subject  is 
included  in  the  class  of  things  which  are  equal  to  two 
right  angles*  The  main  purpose  of  the  proposition 
is  obviously  to  assert  the  necessary  connection  of 


144    HYPOTHETICAL  AND   DISJUNCTIVE  ARGUMENTS 

the  '  triangularity '  and  the  equality  of  angles  with 
two  right  angles,  and  not  to  make  any  direct  asser- 
tion regarding  any  actually  existing  object  .or  group 
of  objects. 

We  reach,  then,  the  following  conclusion :  Our 
thought  is  at  once  both  categorical  and  hypothetical. 
As  categorical,  it  refers  directly  to  objects  and  their 
relations.  The  terms  of  the  proposition  are  then  taken 
in  extension  to  represent  objects  or  groups  of  objects, 
and  the  copula  to  assert  the  inclusion  of  the  subject  in 
the  predicate,  or,  in  cases  of  negative  propositions,  to 
deny  this  relation.  As  hypothetical,  the  reference  to 
things  is  much  more  indirect.  The  terms  of  the  propo- 
sition are  no  longer  regarded  as  representing  objects  or 
classes,  but  are  interpreted  from  the  point  of  view  of 
intension.  The  judgment  affirms  or  denies  the  con- 
nection of  the  qualities  or  attributes  connoted  by  the 
terms,  and  not  that  of  the  objects  which  they  denote. 
Sometimes  the  one  aspect  of  thought,  sometimes  the 
other,  is  most  prominent. 

In  sense-perception  and  in  simple  historical  narra- 
tion, assertions  are  made  directly  and  categorically 
regarding  things  and  eventSc  The  main  interest  is  in 
particular  objects,  persons,  or  events,  and  our  judgments 
refer  directly  and  unambiguously  to  them.  But,  as  we 
have  already  seen,  our  thought  from  its  very  beginning 
attempts  to  get  beyond  the  existence  of  particular  things 
and  events,  and  to  discover  what  qualities  of  objects  are 
necessarily  connected.  We  pass  from  perception  and 
observation  to  explanation,  from  the  narration  of  events, 
to  the  discovery  of  the  law  of  their  connection.  And, 


§41-     DISJUNCTIVE   ARGUMENTS  145 

as  a  result  of  this  advance,  our  judgments  deal  no  longer 
exclusively  with  particular  objects  and  events,  and  the 
fact  of  their  relation,  but  with  the  general  laws  of  the 
connection  between  attributes  and  qualities.  There  is, 
of  course,  no  fixed  point  at  which  we  pass  from  the 
categorical  to  the  hypothetical  aspect  of  thinking.  But, 
in  general,  as  we  pass  from  judgments  of  sense-percep- 
tion and  memory,  to  a  statement  of  theories  and  laws, 
the  hypothetical  element  comes  more  and  more  clearly 
into  the  foreground.  We  have  seen  that  it  is  almost 
impossible  to  interpret  propositions  regarding  geometri- 
cal relations  as  referring  directly  to  classes  of  objects. 
In  the  same  way,  it  is  evident  that  propositions  which 
state  general  laws  are  more  truly  hypothetical  than  cate- 
gorical. When  we  assert  that  '  all  men  are  mortal,'  the 
proposition  does  not  intend  to  state  a  fact  in  regard  to 
each  and  every  man,  or  to  refer  directly  to  individuals 
at  all,  but  to  express  the  essential  and  necessary  relation 
between  humanity  and  mortality.  A  proposition  which 
is  essentially  hypothetical  in  character,  may  then  be 
expressed  in  categorical  form.  It  must  be  remembered 
that  it  is  not  the  form,  but  the  purpose  or  function  of  a 
proposition,  which  determines  its  character.  The  hy- 
pothetical form,  however,  does  justice  to  an  aspect  of 
thought  which  is  especially  prominent  in  the  universal 
laws  and  formulas  of  scientific  knowledge,  and  which 
is  not  adequately  represented  by  the  theory  of  subsump- 
tion,  or  the  inclusion  of  the  subject  in  the  predicate. 

§41.    Disjunctive  Arguments.  —  A  disjunctive   propo- 
sition, as  we  have  already  seen,  is  of  the  form,  *A  is 
L 


146    HYPOTHETICAL  AND   DISJUNCTIVE  ARGUMENTS 

either  B,  or  C,  or  D ' ;  or,  when  expressed  negatively, 
'A  is  neither  B,  nor  C,  nor  D.'  It  is  sometimes  said  to 
be  the  union  of  a  categorical  and  a  hypothetical  propo- 
sition. On  the  one  hand,  it  asserts  categorically  regard- 
ing A,  and  without  reference  to  any  external  condition. 
But  the  disjunctive  proposition  is  not  simple  like  the 
categorical  proposition :  it  states  its  results  as  a  series 
of  related  conditions  and  consequences.  If  A  is  not  B, 
it  tells'  us,  it  must  be  either  C  or  D ;  and  if  it  is  C,  it 
follows  that  it  cannot  be  B  or  D. 

A  disjunctive  proposition  may  at  first  sight  appear  to 
be  a  mere  statement  of  ignorance,  and,  as  such,  to  be 
less  useful  than  the  simple  categorical  judgment  of  per- 
ception. And  it  is  true  that  the  disjunctive  form  may 
be  employed  to  express  lack  of  knowledge.  '  I  do  not 
know  whether  this  tree  is  an  oak  or  an  ash ' ;  '  he  will 
come  on  Monday  or  some  other  day.'  A  true  disjunc- 
tive proposition,  however,  is  not  a  mere  statement  of 
ignorance  regarding  the  presence  or  absence  of  some 
fact  of  perception.  It  is  an  attempt,  on  the  part  of 
intelligence,  to  determine  the  whole  series  of  circum- 
stances or  conditions  within  which  any  fact  of  percep- 
tion may  fall,  and  to  state  the  conditions  in  such  a 
way  that  their  relations  are  at  once  evident.  And  to 
do  this  implies  positive  knowledge.  In  the  first  place, 
the  enumeration  of  possibilities  must  be  exhaustive, 
no  cases  must  be  overlooked,  and  no  circumstances 
left  out  of  account.  Secondly,  the  members  of  the 
proposition  must  be  taken  so  as  to  be  really  disjunc- 
tive. That  is,  they  must  be  exclusive  of  one  another. 
We  cannot  combine  disjunctively  any  terms  we  please 


§4i.     DISJUNCTIVE  ARGUMENTS  147 

with  each  other.  But  it  is  only  when  we  understand 
the  systematic  connections  of  things  in  the  field  in  ques- 
tion, that  we  are  able  to  express  them  in  the  form  either 
B  or  C,  and  thus  assert  that  the  presence  of  one  ex- 
cludes the  other: 

A  disjunctive  proposition,  then,  presupposes  syste- 
matic knowledge,  and  is  consequently  the  expression  of 
a  comparatively  late  stage  in  the  evolution  of  thought. 
It  is  true  that  disjunction  may  involve  doubt  or  igno- 
rance regarding  any  particular  individual.  We  may 
not  be  able  to  say  whether  A  is  B  or  C  or  D.  But, 
before  we  can  formulate  the  disjunctive  proposition, 
we  must  be  already  acquainted  with  the  whole  set  of 
possible  conditions,  and  also  with  the  relation  in  which 
those  conditions  stand  to  each  other.  Our  knowledge, 
when  formulated  in  the  disjunctive  major  premise  of 
an  argument,  is  so  exhaustive  and  systematic,  that 
the  application  to  a  particular  case  effected  by  the 
minor  premise  appears  almost  as  a  tautology.  This 
will  be  evident  in  the  disjunctive  arguments  given 
below. 

There  are  two  forms  of  the  disjunctive  syllogism. 
The  first  is  sometimes  called  the  modus  tollendo  ponens, 
or  the  mood  which  affirms  by  denying.  The  minor 
premise,  that  is,  is  negative,  and  the  conclusion  affirma- 
tive. The  form  is,  — 

A  is  either  B  or  C, 

A  is  not  C, 

Therefore  A  is  B. 

The  negative  disjunctive  argument  has  an  affirmative 
minor  premise.  It  is  known  as  the  modus  ponendo 


148     HYPOTHETICAL  AND   DISJUNCTIVE  ARGUMENTS 

tollens,  or  the  form  which,  by  affirming  one  member  oi 
the  disjunctive  series,  denies  the  others,  — 

A  is  B  or  C  or  D, 

But  A  is  B, 

Therefore  A  is  neither  C  nor-  D. 

It  is,  of  course,  a  very  simple  matter  to  draw  the  con- 
clusion from  the  premises  in  these  cases.  As  we  have 
already  indicated,  the  real  intellectual  work  consists  in 
obtaining  the  premises,  especially  in  discovering  the 
relations  enumerated  in  the  major  premise.  It  is  in 
formulating  the  major  premise,  too,  that  errors  are  most 
likely  to  arise.  As  already  pointed  out,  it  is  essential 
that  the  disjunctive  members  shall  be  exhaustively 
enumerated,  and  also  that  they  shall  exclude  each  other. 
But  it  is  not  always  easy  to  discover  all  the  possibilities 
of  a  case,  or  to  formulate  them  in  such  a  way  that  they 
are  really  exclusive.  If  we  say,  '  he  is  either  a  knave 
or  a  fool,'  we  omit  the  possibility  of  his  being  both  the 
one  and  the  other  to  some  extent.  A  great  many  state- 
ments which  are  expressed  in  the  form  of  disjunctive 
propositions  are  not  true  logical  disjunctives.  Thus  we 
might  say,  'every  student  works  either  from  love  of 
learning,  or  from  love  of  praise,  or  for  the  sake  of  some 
material  reward.'  But  the  disjunction  does  not  answer 
the  logical  requirements,  for  it  is  possible  that  two  or 
more  of  these  motives  may  influence  his  conduct  at 
the  same  time.  The  disjunctive  members  are  neither 
exclusive  nor  completely  enumerated. 

§  42.  The  Dilemma.  —  A  dilemma  is  an  argument 
composed  of  hypothetical  and  disjunctive  propositions. 


§42.    THE   DILEMMA  149 

As  the  word  is  used  in  ordinary  life,  we  are  said  to  be  in 
a  dilemma  whenever  there  are  but  two  courses  of  action 
open  to  us,  and  when  both  of  these  have  unpleasant 
consequences.  In  the  same  way,  the  logical  dilemma 
shuts  us  in  to  a  choice  between  alternatives,  either  of 
which  leads  to  a  conclusion  we  would  gladly  avoid. 

The  first  form,  which  is  sometimes  called  the  Simple 
Constructive  Dilemma,  yields  a  simple  or  categorical  con- 
clusion, — 

If  A  is  B,  C  is  D ;  and  if  E  is  F,  C  is  D, 
But  either  A  is  B,  or  E  is  F, 

Therefore  C  is  D. 

It  will  be  noticed  that  the  minor  premise  affirms  dis- 
junctively the  antecedents  of  the  two  hypothetical  prop- 
ositions which  form  the  major  premise,  and  that  the 
conclusion  follows  whichever  alternative  holds.  We 
may  take  as  a  concrete  example  of  this  type  of  argu- 
ment :  — 

If  a  man  acts  in  accordance  with  his  own  judgment,  he  will  be 
criticised ;  and  if  he  is  guided  by  the  opinions  and  rules  of  others, 
he  will  be  criticised. 

But  he  must  either  act  in  accordance  with  his  own  judgment,  or 
be  guided  by  the  opinions  of  others. 

Therefore,  in  any  case,  he  will  be  criticised. 

The  hypothetical  propositions  which  make  up  the 
major  premise  of  a  dilemma  do  not  usually  have  the 
same  consequent,  as  is  the  case  in  the  examples  just 
given.  When  the  consequents  involved  are  different, 
the  dilemma  is  said  to  be  complex,  and  the  conclusion 
has  the  form  of  a  disjunctive  proposition.  In  the  Complex 


150     HYPOTHETICAL  AND   DISJUNCTIVE  ARGUMENTS 

Constructive  Dilemma,  the  minor  premise  affirms  disjunc- 
tively the  antecedents  of  the  major,  and  the  conclusion 
is  consequently  affirmative.  We  may  take,  as  an  ex- 
ample, the  argument  by  which  the  Caliph  Omar  is 
said  to  have  justified  the  burning  of  the  Alexandrian 
library :  - 

If  these  books  contain  the  same  doctrines  as  the  Koran,  they  are 
unnecessary ;  and  if  they  are  at  variance  with  the  Koran,  they  are 
wicked  and  pernicious. 

But  they  must  either  contain  the  same  doctrines  as  the  Koran  or 
be  at  variance  with  it. 

Therefore  these  books  are  either  unnecessary  or  wicked  and  per- 
nicious. 

A  third  form,  the  Complex  Destructive  Dilemma,  obtains 
a  negative  disjunctive  proposition  as  a  conclusion,  by 
denying  the  consequents  of  the  hypothetical  proposi- 
tions which  form  the  major  premise  of  the  argument. 
We  may  take  the  following  example :  — 

If  a  man  is  prudent,  he  will  avoid  needless  dangers ;  if  he  is  bold 
and  courageous,  he  will  face  dangers  bravely. 

But  this  man  neither  avoids  needless  dangers  nor  does  he  face 
dangers  bravely. 

Therefore  he  is  neither  prudent  nor  bold  and  courageous. 

By  taking  more  than  two  hypothetical  propositions 
as  major  premise,  we  may  obtain  a  Trilemma,  a  Tetra- 
lemma,  or  a  Polylemma.  These  forms,  however,  are 
used  much  less  frequently  than  the  Dilemma. 

The  dilemma  is  essentially  a  polemical  or  contro- 
versial form  of  argument.  Its  object,  as  we  have  seen, 
is  to  force  an  unwelcome  conclusion  upon  an  adversary, 
by  showing  that  his  argument,  or  his  conduct,  admits  of 


§42.     THE   DILEMMA  151 

one  or  other  of  two  unpleasant  interpretations.  We 
sometimes  speak  of  the  horns  of  the  dilemma,  and  of 
our  adversary  as  '  gored,'  whichever  horn  he  may  choose. 
Dilemmas,  however,  like  all  controversial  arguments, 
are  more  often  fallacious  than  valid.  The  minor  pre- 
mise of  a  dilemmatic  argument,  as  we  have  already 
seen,  is  a  disjunctive  proposition  with  two  members. 
But  it  is  very  rarely  that  two  alternatives  exhaust  all 
the  possible  cases.  The  cases  enumerated,  too,  may 
not  exclude  each  other,  or  be  real  alternatives  at  all. 
The  dilemma  is  thus  subject  to  all  the  dangers  which 
we  have  already  noticed  in  the  case  of  the  disjunctive 
argument.  In  addition,  it  is  necessary  to  see  that  the 
canon  of  the  hypothetical  syllogism,  'affirm  the  ante- 
cedent or  deny  the  consequent,'  is  observed.  If  this 
rule  is  not  observed,  the  logical  form  of  the  argument 
will  not  be  correct. 

References,  especially  for  §  40 

J.  S.  Mill,  Logic,  Bk.  I.  Ch.  V. 
C.  Sigwart,  Logic,  Ft.  I.  Ch.  VII. 

W.   Minto,   Logic  Inductive  and  Deductive,  pp.    129-138,  and 
pp.  214-225. 

F.  H.  Bradley,  The  Principles  of  Logic,  Bk.  I.  Ch.  2. 
B.  Bosanquet,  The  Essentials  of  Logic,  Lecture  VI. 


CHAPTER   XII 

FALLACIES    OF    DEDUCTIVE    REASONING 

§  43.  Classification  of  Fallacies. — We  shall  hereafter 
treat  of  the  fallacies  or  errors  to  which  inductive  reason- 
ing is  most  subject  (Ch.  xix.).  At  present,  however, 
it  is  necessary  to  consider  the  fallacies  which  are  likely 
to  attend  the  employment  of  the  syllogistic  form  of 
reasoning.  In  considering  the  subject,  we  shall  find 
that  many  fallacies  belong  equally  to  both  kinds  of 
reasoning.  This  is  especially  true  of  errors  which  arise 
from  the  careless  use  of  words. 

The  first  systematic  account  of  fallacies  is  given  in 
Aristotle's  treatise,  On  Sophistical  Difficulties  (jrepl  aofacr- 
TLK&V  eXeyxtov).  In  this  work,  Aristotle  divides  falla- 
cies into  two  classes  :•  those  which  are  due  to  language 
(jrapa  TTJV  \e%iv,  or,  as  they  are  usually  called,  fallacies 
in  dictione\  and  those  which  are  not  connected  with  lan- 
guage (ef co  TT)?  Xe'feco?,  extra  dictionem).  Under  the  first 
head,  he  enumerates  six  kinds  of  fallacies,  and  under 
the  second,  seven.  Aristotle's  principle  of  classification 
is,  however,  not  entirely  satisfactory.  We  must  try  to 
find  some  positive  principle  or  principles  of  classification 
which  will  render  us  more  assistance  in  understanding 
the  relations  between  the  various  fallacies  than  is 
afforded  by  Aristotle's  division  into  those  which  belong 
to  language,  and  those  which  do  not. 

152 


§43-     CLASSIFICATION   OF   FALLACIES  153 

In  the  strict  sense  of  the  word,  a  fallacy  is  to  be 
defined  as  an  error  in  reasoning.  In  the  syllogism, 
however,  propositions  or  premises  form  the  data  or 
starting-point.  If,  now,  these  propositions  are  not 
properly  understood,  the  conclusions  to  which  they 
lead  are  likely  to  be  false.  We  may  then  first  divide 
fallacies  into  Errors  of  Interpretation,  and  Fallacies  in 
Reasoning.  Errors  in  interpreting  propositions  might, 
perhaps,  be  more  properly  treated  in  a  work  on  rhetoric 
than  in  a  chapter  on  logical  fallacies.  But  it  has  been 
the  custom  ever  since  the  time  of  Aristotle  to  include 
in  the  enumeration  of  logical  fallacies  a  number  of 
errors  which  are  likely  to  arise  in  interpreting  propo- 
sitions. Moreover,  as  we  saw  in  Chapter  VII.,  there 
are  certain  processes  of  interpretation,  like  Obversion 
and  Conversion,  which  are  sometimes  called  immediate 
inference,  and  which  require  a  knowledge  of  the  logical 
structure  of  propositions. 

The  Fallacies  which  arise  in  the  process  of  reasoning, 
we  may  again  divide  into  Formal  Fallacies,  or  violations 
of  the  syllogistic  rules,  and  Material  Fallacies.  The 
latter  class  may  be  further  divided  into  Fallacies  of 
Equivocation  (including  Ambiguous  Middle,  Composi- 
tion, Division,  and  Accident)  and  Fallacies  of  Presump- 
tion (including  Petitio  Principii,  Irrelevant  Conclusion, 
Non  Sequitur,  and  Complex  Questions).  The  following 
table  will  summarize  this  classification  :  — 


154 


FALLACIES   OF   DEDUCTIVE   REASONING 


FALLACIES 


Errors  in  Interpretation 
(i)   Illogical  Obversion  or 


Mistakes  in  Reasoning 


Conversion 

(2)  Amphiboly 

(3)  Accent 

Mat 

'.rial 

Forn 

tal 

Equivo 

cation 

Presu, 

nption 

f(0 

Four  Terms 

(i)  Ambiguous 

(0 

Petitio  Prin- 

(2) 

Undistributed 

Middle 

cipii 

In  Categorical 

Middle 

(2)  Composition 

(2) 

Complex 

Arguments 

(3) 

Illicit  Major 

(3)  Division 

Question 

(4) 

Illicit  Minor 

(4)  Accident 

(3) 

Irrelevant 

.(5) 

Negative  Premises 

Conclusion 

In 

Hypothetical- 
Arguments 

(6) 

l(7) 

Denying  the  Antecedent 
Affirming  the  Consequent 

(4) 

Non 

Sequitur 

In  Disjunctive 

(8) 

Imperfect  Disjunction 

Arguments 

§  44.  Errors  in  Interpretation.  —  This  class  of  fallacies 
results  from  imperfect  understanding  of  the  meaning 
of  propositions.  They  are  not,  then,  strictly  speaking, 
errors  of  reasoning  at  all.  If,  however,  the  propositions 
employed  as  premises  in  an  argument  are  not  correctly 
understood,  the  conclusions  founded  upon  them  are 
likely  to  be  erroneous.  And  even  if  the  proposition, 
which  is  wrongly  interpreted,  is  not  made  the  basis  of 
further  reasoning,  it  is  in  itself  the  result  of  an  intel- 
lectual error  against  which  it  is  possible  to  guard.  We 
do  not,  of  course,  profess  to  point  out  all  the  possible 
sources  of  error  in  interpreting  propositions.  The  only 


§44-     ERRORS  IN   INTERPRETATION  155 

rule  applicable  to  all  cases  which  can  be  given  is  this : 
Accept  no  proposition  until  you  understand  its  exact 
meaning;  and  know  precisely  what  it  implies.  Delib- 
eration and  attention,  both  with  regard  to  our  own 
statements  and  those  of  others,  are  the  only  means 
of  escaping  errors  of  this  kind. 

(i)  Illogical  Obversion  or  Conversion.  —  In  a  previous 
chapter  (Ch.  vii.),  we  have  treated  of  Obversion  and 
Conversion,  and  shown  the  rules  to  be  followed  in  stating 
the  obverse  or  the  converse  of  a  proposition.  In  Obver- 
sion, we  interpret  or  show  what  is  involved  in  a  proposi- 
tion, by  stating  its  implications  in  a  proposition  of  the 
opposite  quality.  And  unless  we  have  clearly  grasped 
the  meaning  of  the  original  proposition,  mistakes  are 
likely  to  arise  in  changing  from  the  affirmative  to  the 
negative  form  of  statement,  or  from  the  negative  to  the 
affirmative.  Thus,  we  should  fall  into  an  error  of  this 
kind  if  we  should  take  the  proposition,  'honesty  is 
always  good  policy,'  to  be  the  equivalent  of,  or  to  imply, 
the  statement,  'dishonesty  is  always  bad  policy.'  Nor 
can  we  obtain  by  obversion  the  proposition,  *  all  citizens 
are  allowed  to  vote,'  from,  'no  aliens  are  allowed  to 
vote.' 

In  Conversion,  we  take  some  proposition,  A  is  B,  and 
ask  what  assertion  it  implies  regarding  the  predicate. 
Does  '  all  brave  men  are  generous '  imply  also  that  '  all 
generous  men  are  brave '  ?  This  is,  perhaps,  the  most 
frequent  source  of  error  in  the  conversion  of  proposi- 
tions. I  do  not  mean  that  in  working  logical  examples 
we  are  likely  to  convert  proposition  A  simply,  instead  of 
by  limitation.  But  in  the  heat  of  debate,  or  when  using 


156  FALLACIES   OF  DEDUCTIVE   REASONING 

propositions  without  proper  attention,  there  is  a  natural 
tendency  to  assume  that  a  proposition  which  makes  a 
universal  statement  regarding  the  subject,  does  the  same 
with  regard  to  the  predicate.  And,  although  such  errors 
are  very  obvious  when  pointed  out,  —  as,  indeed,  is  the 
case  with  nearly  all  logical  fallacies,  —  they  may  very 
easily  impose  upon  us  when  our  minds  are  not  fully 
awake,  that  is,  when  attention  is  not  active  and  con- 
sciously on  guard.  Of  the  other  methods  of  conversion 
perhaps  contraposition  is  most  likely  to  be  a  source  of 
error.  We  have  already  (§  27)  given  the  rules  for  ob- 
taining the  contrapositive  of  any  proposition.  Some 
practice  in  working  examples  will  assist  students  in 
perceiving  what  is  the  logical  contrapositive  to  any 
proposition,  and  in  detecting  fallacies. 

(2)  Amphiboly,  or  amphibology  (a/n^t/SoXta),  consists 
in   misconception    arising   from    the    ambiguous  gram- 
matical construction  of  a  proposition.     A  sentence  may 
have   two    opposite    meanings,  but  one  may   be  more 
natural  and  prominent  than  the  other.     A  deception 
may  be  practised   by  leading  a  person  to  accept  the 
meaning  more  strongly  suggested,  while  the  significance 
intended  is  the  very  opposite,  as,  e.g.,  '  I  hope  that  you 
the  enemy  will  slay.'     In  Shakespeare's  Henry  VI. ,  we 
have  an  instance  of  amphiboly  in  the  prophecy  of  the 
spirit,    that    "the    Duke    yet    lives    that    Henry   shall 
depose." 

(3)  The  Fallacy  of  Accent  is  a  misconception  due  to 
the  accent  or  emphasis  being  placed  upon  the  wrong 
words  in  a  sentence.     It  may,  therefore,  be  regarded 
as  a  rhetorical,  rather  than  as  a  logical  fallacy.    Jevons's 


§45-     FORMAL   FALLACIES  157 

examples  of  this  fallacy  may  be  quoted  in  part.  "  A 
ludicrous  instance  is  liable  to  occur  in  reading  Chapter 
XIII.  of  the  First  Book  of  Kings,  verse  27,  where  it  is 
said  of  the  prophet,  '  And  he  spake  to  his  sons,  saying, 
Saddle  me  the  ass.  And  they  saddled  him'  The  italics 
indicate  that  the  word  him  was  supplied  by  the  trans- 
lators of  the  authorized  version,  but  it  may  suggest  a 
very  different  meaning.  The  commandment,  'Thou 
shalt  not  bear  false  witness  against  thy  neighbour/  may 
be  made  by  a  slight  emphasis  of  the  voice  on  the  last 
word  to  imply  that  we  are  at  liberty  to  bear  false 
witness  against  other  persons.  Mr.  De  Morgan  who 
remarks  this  also  points  out  that  the  erroneous  quoting 
of  an  author,  by  unfairly  separating  a  word  from  its 
context,  or  italicizing  words  which  were  not  intended  to 
be  italicized,  gives  rise  to  cases  of  this  fallacy."  1  Jevons 
is  also  authority  for  the  statement  that  Jeremy  Bentham 
was  so  much  afraid  of  being  led  astray  by  this  fallacy 
that  he  employed  a  person  to  read  to  him  whose  voice 
and  manner  of  reading  were  particularly  monotonous. 

§  45.  Formal  Fallacies.  — We  shall  follow  our  table, 
and  deal  with  mistakes  of  Reasoning  under  the  two 
headings  of  Formal  Fallacies,  and  Material  Fallacies. 
Formal  fallacies  arise  from  violations  of  the  rules  of  the 
syllogism.  The  breaches  of  these  rules  have  been 
already  pointed  out,  and  illustrated  in  our  discussion  of 
the  various  forms  of  syllogistic  argument.  The  analysis 
of  arguments,  with  a  view  to  the  detection  of  such 
fallacies,  where  any  exist,  is  a  very  important  exercise, 

1  Jevons,  Lessons  in  Logic,  p.  1 74. 


158  FALLACIES   OF  DEDUCTIVE   REASONING 

and  affords  valuable  mental  discipline.  It  seems  only 
necessary  here  to  add  a  remark  regarding  the  first 
fallacy  on  our  list,  that  of  Four  Terms,  or  Quaternio 
Terminorum,  as  it  is  usually  called  by  logicians. 

The  first  canon  of  the  categorical  syllogism  states 
that  'a  syllogism  must  contain  three  and  only  three 
terms.'  This  rule  would  of  course  be  violated  by  such 
an  argument  as,  — 

Frenchmen  are  Europeans, 
Englishmen  are  Anglo-Saxons, 


Therefore  Englishmen  are  Europeans. 

It  is  so  obvious  that  this  example  does  not  contain 
a  real  inference  that  no  one  would  be  likely  to  be  mis- 
led by  the  pretence  of  argument  which  it  contains.  In 
some  cases,  however,  a  term  may  be  used  in  two  senses, 
although  the  words  by  which  it  is  expressed  are  the 
same.  The  following  example  may  be  given :  — 

Every  good  law  should  be  obeyed, 
The  law  of  gravitation  is  a  good  law, 

Therefore  the  law  of  gravitation  should  be  obeyed. 

Here  we  have  really  four  terms.  The  word  'law,'  in 
the  first  proposition,  means  a  command  given  or  enact- 
ment made  by  some  persons  in  authority.  A  'good 
law'  in  this  sense  then  means  a  just  law,  or  one  which 
has  beneficial  results.  But  in  the  second  proposition 
it  signifies  a  statement  of  the  uniform  way  in  which 
phenomena  behave  under  certain  conditions.  A  '  good 
law'  from  this  point  of  view  would  imply  a  correct 
statement  of  these  uniformities.  It  is  interesting  to 
note  that  this  example  may  also  be  regarded  as  an 


§  46.     MATERIAL  FALLACIES  1 59 

instance  of  Equivocation,  and  classified  as  a  case  of  an 
ambiguous  middle  term.  It  is  often  possible  to  classify 
a  fallacy  under  more  than  a  single  head. 

There  are,  however,  cases  where  an  argument  may 
seem  at  first  sight  to  have  four  terms,  but  where  the 
defect  i£  only  verbal.  The  matter  must,  of  course,  be 
determined  by  reference  to  the  meaning  of  terms  and 
not  merely  to  the  verbal  form  of  expression.  It  is  ideas 
or  concepts,  and  not  a  form  of  words,  which  are  really 
operative  in  reasoning. 

§  46.  Material  Fallacies.  — What  are  called  material 
fallacies  do  not  result  from  the  violation  of  any  specific 
logical  rules.  They  are  usually  said  to  exist,  not  in  the 
form,  but  in  the  matter  of  the  argument.  Consequently, 
it  is  sometimes  argued,  the  detection  and  description  of 
them  do  not  properly  belong  to  logic  at  all.  We  have 
found,  however,  that  all  these  fallacies  have  their 
source  in  Equivocation  and  Presumption.  They  thus 
violate  two  of  the  fundamental  principles  of  logical 
argument.  For  all  logical  reasoning  presupposes  that 
the  terms  employed  shall  be  clearly  defined,  and  used 
throughout  the  argument  with  a  fixed  and  definite 
signification.  And,  secondly,  logic  requires  that  the 
conclusion  shall  not  be  assumed,  but  derived  strictly 
from  the  premises.  The  violation  of  these  principles 
is,  therefore,  a  proper  matter  of  concern  to  the  logician. 
We  shall  treat  first  of  the  fallacies  of  Equivocation. 

(A)  The  fallacies  of  Equivocation  have  been  enumer- 
ated as  Ambiguous  Middle  Term,  Composition,  Division, 
and  Accident.  These  all  result  from  a  lack  of  clearness 


160  FALLACIES   OF  DEDUCTIVE  REASONING 

and  definiteness  in  the  terms  employed.     We  shall  deal 
with  them  briefly  in  order. 

(1)  The   phrase,  Ambiguous   Middle   Term,  describes 
the  first  fallacy  of  this  group.     It  is  obvious  that  the 
middle  term   cannot   form  a  proper  standard  of  com- 
parison  if   its    meaning    is    uncertain    or   shifting.     A 
standard  of  measure  must  be  fixed  and  definite.     One 
illustration  of  this  fallacy  will  be  sufficient :  — 

Partisans  are  not  to  be  trusted, 
Democrats  are  partisans, 

Therefore  Democrats  are  not  to  be  trusted. 
The  middle  term,  'partisan,'  is  evidently  used  in  two 
senses  in  this  argument.  In  the  first  premise  it  signifies 
persons  who  are  deeply  or  personally  interested  in  some 
measure ;  and  in  the  latter  it  simply  denotes  the 
members  of  a  political  party.  When  an  argument  is 
long,  and  is  not  arranged  in  syllogistic  form,  this  fallacy 
is  much  more  difficult  of  detection  than  in  the  simple 
example  which  has  been  given.  It  is  of  the  utmost 
importance,  then,  to  insist  on  realizing  clearly  in  con- 
sciousness the  ideas  for  which  each  term  stands,  and  not 
to  content  ourselves  with,  following  the  words. 

(2)  The  fallacy  of  Composition  arises  when  we  affirm 
something  to  be  true  of  a  whole,  which  holds  true  only 
of  one  or  more  of  its  parts  when  taken  separately  or 
distributive ly.     Sometimes  the  error  is  due  to  confusion 
between  the  distributive  and  collective  signification  of 
'  all/  as  in  the  following  example  :  — 

All  the  angles  of  a  triangle  are  less  than  two  right  angles, 
A,  B,  and  C  are  all  the  angles  of  this  triangle, 

Therefore  A,  B,  and  C  are  less  than  two  right  angles. 


§  46.     MATERIAL  FALLACIES  l6l 

It  is,  of  course,  obvious  that  '  all  the  angles  of  a 
triangle '  in  the  major  premise  signifies  each  and  every 
angle  when  taken  by  itself,  and  that  the  same  words  in 
the  minor  premise  signify  all  the  angles  collectively. 
What  is  true  of  all  the  parts  taken  separately,  is  not 
necessarily  true  of  the  whole.  We  cannot  say  that 
because  no  one  member  of  a  jury  is  very  wise  or  very 
fair-minded,  that  the  jury  as  a  whole  are  not  likely  to 
bring  in  a  just  verdict.  The  members  may  mutually 
correct  and  supplement  each  other,  so  that  the  finding 
of  the  jury  as  a  whole  will  be  much  fairer  and  wiser 
than  the  judgment  of  any  single  individual  composing 
it.  Another  instance  of  this  fallacy  which  is  often 
quoted  is  that  by  which  protective  duties  are  sometimes 
supported :  — 

The  manufacturers  of  woollens  are  benefited  by  the  duty  on 
woollen  goods  ;  the  manufacturers  of  cotton  by  the  duty  on  cotton ; 
the  farmer  by  the  duties  on  wool  and  grain ;  and  so  on  for  all  the 
other  producing  classes  ;  therefore,  if  all  the  products  of  the  country 
were  protected  by  an  import  duty,  all  the  producing  classes  would 
be  benefited  thereby. 

But,  because  each  class  would  be  benefited  by  an  import 
tax  upon  some  particular  product,  it  does  not  necessarily 
follow  that  the  community  as  a  whole  would  be  benefited 
if  all  products  were  thus  protected.  For,  obviously,  the 
advantages  which  any  class  would  obtain  might  be  more 
than  offset  by  the  increased  price  of  the  things  which 
they  would  have  to  buy.  On  the  other  hand,  it  would 
be  necessary  to  take  into  consideration  the  fact  that  an 
increase  in  the  prosperity  of  one  class  indirectly  brings 
profit  to  all  the  other  members  of  the  same  society. 


1 62  FALLACIES  OF  DEDUCTIVE  REASONING 

We  cannot  regard  a  whole  as  simply  a  sum  of  parts, 
but  must  consider  also  the  way  in  which  the  parts  act 
and  react  upon  each  other.  9 

(3)  The  fallacy  of  Division  is  the  converse  of  Com- 
position. It  consists  in  assuming  that  what  is  true  of 
the  whole  is  also  true  of  the  parts  taken  separately. 
Some  term,  which  is  used  in  the  major  premise  collec- 
tively, is  employed  in  a  distributive  sense  in  the  minor 
premise  and  conclusion.  The  following  example  will 
illustrate  this :  — 

All  the  angles  of  a  triangle  are  equal  to  two  right  angles, 
A  is  an  angle  of  a  triangle, 

Therefore  A  is  equal  to  two  right  angles. 

To  argue  that,  because  some  measure  benefits  the 
country  as  a  whole,  it  must  therefore  benefit  every 
section  of  the  country,  would  be  another  instance  of 
this  fallacy.  Again,  we  may  often  find  examples  of 
both  Division  and  Composition  in  the  practice  so  com- 
mon in  debate  of  '  taking  to  pieces '  the  arguments  by 
which  any  theory  or  proposed  course  of  action  is  justi- 
fied. A  person  would  be  guilty  of  Division  if  he  should 
argue  that,  because  a  complex  theory  is  not  completely 
proved,  none  of  the  arguments  by  which  it  is  supported 
have  any  value.  It  is,  however,  perhaps  more  common 
to  fall  into  the  fallacy  of  Composition  in  combating  the 
arguments  of  an  opponent.  Some  measure,  for  example, 
is  proposed  to  which  a  person  finds  himself  in  opposi- 
tion. It  is  usually  easy  to  analyze  the  different  argu- 
ments which  have  been  advanced  in  support  of  the 
measure,  and  to  show  that  no  single  one  of  these  taken 


§46.     MATERIAL   FALLACIES  163 

by  itself  is  sufficient  to  justify  the  change.  The  con- 
clusion may  then  be  drawn  with  a  fine  show  of  logic 
that  all  the  reasons  advanced  have  been  insufficient. 
This,  of  course,  is  to  neglect  the  cumulative  effect  of 
the  arguments ;  it  is  to  assume  that  what  is  true  of 
'  all,'  taken  distributively,  is  also  true  of  '  all '  when 
taken  in  conjunction. 

(4)  It  is  often  difficult  to  distinguish  the  various  forms 
of  the  fallacy  of  Accident  from  Composition  and  Divi- 
sion. We  have  seen  that  the  latter  rest  upon  a  confu- 
sion between  whole  and  part;  or,  as  we  have  already 
expressed  it,  on  an  equivocation  between  the  distributive 
and  collective  use  of  terms.  The  fallacies  of  Accident 
are  also  due  to  Equivocation.  But  in  this  case  the  con- 
fusion is  between  essential  properties  and  accidents, 
between  what  is  true  of  a  thing  in  its'  real  nature,  as 
expressed  by  its  logical  definition,  and  what  is  true  of  it 
only  under  some  peculiar  or  accidental  circumstance. 

Tnere  are  two  forms  of  this  argument  which  are 
usually  recognized :  (a)  The  Direct  or  Simple  Fallacy 
of  Accident,  which  consists  in  arguing  that  what  is  true 
of  a  thing  generally  is  also  true  of  it  under  some  acci- 
dental or  peculiar  circumstance.  The  old  logicians 
expressed  this  in  the  formula,  a  dicto  simpliciter  ad 
dictum  secundum  quid.  The  second  form  is  (b)  the 
Converse  Fallacy  of  Accident,  which  consists  in  arguing 
that  what  is  true  of  a  thing  under  some  condition  or 
accident,  can  be  asserted  of  it  simply,  or  in  its  essential 
nature.  The  formula  for  this  is,  a  dicto  secundum  quid 
&d  dictum  simpliciter. 

.It  would  be   an  illustration  of  the  direct  fallacy  to 


1 64  FALLACIES   OF   DEDUCTIVE   REASONING 

reason,  that  because  man  is  a  rational  being,  there- 
fore a  drunken  man  or  an  angry  man  will  be  guided  by 
reason.  Similarly,  we  should  commit  this  fallacy  if 
we  were  to  argue  that  because  beefsteak  is  wholesome 
food,  it  would  be  good  for  a  person  suffering  with  fever 
or  dyspepsia ;  or  to  conclude  from  the  principle  that 
it  is  right  to  relieve  the  suffering  of  others,  that  we 
ought  to  give  money  to  beggars. 

It  would  be  a  case  of  the  converse  fallacy  to  argue, 
that  because  spirituous  liquors  are  of  value  in  certain 
cases  of  disease,  they  must  therefore  be  beneficial  to  a 
person  who  is  well.  We  should  also  be  guilty  of  the 
same  fallacy  if  we  should  conclude  that  it  is  right  to 
deceive  others,  from  the  fact  that  it  is  sometimes  neces- 
sary to  keep  the  truth  from  a  person  who  is  sick,  or  to 
deceive  an  enemy  in  time  of  war. 

The  fallacies  of  Accident,  like  all  the  fallacies  of 
Equivocation,  are  largely  the  result  of  a  loose  and  care- 
less use  of  language.  By  qualifying  our  terms  so  as 
to  state  the  exact  circumstances  involved,  they  may 
easily  -be  detected  and  avoided. 

(B)  Fallacies  of  Presumption.  —  The  fallacies  of  this 
group  are  the  result  of  presumption  or  assumption  on 
the  part  of  the  person  making  the  argument.  It  is  pos- 
sible (i)  to  assume  the  point  to  be  proved,  either  in 
the  premises  of  an  argument,  or  in  a  question  (Petitio 
Principii,  and  Complex  Question);  or  (2)  to  assume 
without  warrant  that  a  certain  conclusion  follows  from 
premises  which  have  been  stated  (Non  Sequitur)\  or 
(3)  that  the  conclusion  obtained  proves  the  point  at 
issue  (Irrelevant  Conclusion), 


§  46.     MATERIAL  FALLACIES  165 

(i)  Petitio  Principii,  or  'Begging  the  Question,'  is  a 
form  of  argument  which  assumes  the  conclusion  to  be 
proved.  This  may  be  done  in  either  of  two  ways, 
(i)  We  may  postulate  the  fact  which  we  wish  to  prove, 
or  its  equivalent  under  another  name.  Thus,  for  ex- 
ample, we  might  argue  that  an  act  is  morally  wrong 
because  it  is  opposed  to  sound  ethical  principles.  'The 
soul  is  immortal  because  it  is  a  simple  and  indecom- 
posable substance,'  may  be  regarded  as  another  ex- 
ample of  this  assumption.  But  (2)  the  question  may 
be  begged  by  making  a  general  assumption  covering 
the  particular  point  in  dispute.  Thus,  if  the  advisa- 
bility of  legislation  regulating  the  hours  of  labor  in  a 
mine  or  factory  were  under  discussion,  the  question- 
begging  proposition,  '  all  legislation  which  interferes 
with  the  right  of  free  contract  is  bad,'  might  be  pro- 
pounded as  a  settlement  of  the  whole  question. 

A  special  form  of  this  fallacy  results  when  each  of 
two  propositions  is  used  in  turn  to  prove  the  truth  of 
the  other.  This  is  known  as  'reasoning  in  a  circle,' 
or  circulus  in  probando.  This  method  of  reasoning  is 
often  adopted  when  the  premise,  which  has  been  em- 
ployed to  prove  the  first  conclusion,  is  challenged.  '  I 
should  not  do  this  act,  because  it  is  wrong.'  '  But  how 
do  you  know  that  the  act  is  wrong  ? '  '  Why,  because 
I  know  that  I  should  not  do  it.' 

It  is  always  necessary,  then,  to  see  that  the  conclu- 
sion has  not  been  assumed  in  the  premises.  But,  since 
the  conclusion  always  follows  from  the  premises,  we 
may  say  in  one  sense  that  the  conclusion  is  always  thus 
assumed.  It  is,  therefore,  easy  to  charge  an  opponent 


1 66  FALLACIES   OF   DEDUCTIVE   REASONING 

unjustly  with  begging  the  question.  De  Morgan  in  his 
work  on  Fallacies,  says  :  "  There  is  an  opponent  fallacy 
to  the  Petitio  Principii  which,  I  suspect,  is  of  more 
frequent  occurrence :  it  is  the  habit  of  many  to  treat 
an  advanced  proposition  as  a  begging  of  the  question 
the  moment  they  see  that,  if  established,  it  would  es- 
tablish the  question."  All  argument  must,  of  course, 
start  from  premises  to  which  both  parties  assent.  But 
candour  and  fairness  forbid  us  to  charge  an  opponent 
with  Petitio  because  the  results  of  his  premises  are 
unwelcome.  It  was  Charles  Lamb  who  humorously 
remarked  that  he  would  not  grant  that  two  and  two 
are  four  until  he  knew  what  use  was  to  be  made  of 
the  admission. 

(2)  The  Complex  Question  is  an  interrogative  form  of 
Petitio,     It  is  not  really  a  simple  interrogation,  but  is 
founded  upon  an  assumption.     Examples  may  be  found 
in  popular  pleasantries,  such  as,  '  Have  you  given  up 
your  drinking  habits  ? '     'Do  the  people  in  your  part  of 
the  country  still  carry  revolvers  ? '   Disjunctive  questions, 
too,  always  contain  an  assumption  of  this  kind :  'Is  this 
an    oak    or    an    ash  ? '     '  Does    he   live    in    Boston   or 
New  York  ? '     The  '  leading  questions  '  which  lawyers 
frequently  use  in  examining  witnesses,  but  which  are 
always  objected  to  by  the  opposing  counsel,  are  usually 
of  this  character.     Further  instances  may  perhaps  be 
found  in  the  demand  for  explanation  of  facts  which  are 
either  false,  or  not  fully  substantiated;   as,  e.g.  'Why 
does  a  fish  when  dead  weigh  more  than  when  alive  ? ' 
1  What  is  the  explanation  of  mind-reading  ? ' 

(3)  The   Irrelevant   Conclusion,  or   Ignoratio   Elenchi, 


§46.     MATERIAL  FALLACIES  1 67 

consists  in  substituting  for  the  conclusion  to  be  proved 
some  other  proposition  more  or  less  nearly  related  to  it 
This  fallacy  may  be  the  result  of  an  involuntary  con- 
fusion on  the  part  of  the  person  employing  it,  or  it  may 
be  consciously  adopted  as  a  controversial  stratagem  to 
deceive  an  opponent  or  an  audience.  When  used  in 
this  latter  way,  it  is  usually  intended  to  conceal  the 
weakness  of  a  position  by  diverting  attention  from  the 
real  point  at  issue.  This  is,  indeed,  a  favourite  device 
of  those  who  have  to  support  a  weak  case.  A  counsel 
for  the  defence  in  a  law-suit  is  said  to  have  handed 
to  the  barrister  presenting  the  case  the  brief  marked, 
'  No  case ;  abuse  the  plaintiff's  attorney.'  To  answer 
a  charge  or  accusation  by  declaring  that  the  person 
bringing  the  charge  is  guilty  of  as  bad,  or  even  worse, 
things,  —  what  is  sometimes  called  the  tu  quoque  form 
of  argument  —  is  also  an  example  of  this  fallacy. 

Apart  from  such  wilful  perversions  or  confusions, 
many  unintentional  instances  of  this  fallacy  occur.  In 
controversial  writing,  it  is  very  natural  to  assume  that 
a  proposition  which  has  some  points  of  connection  with 
the  conclusion  to  be  established,  is  'essentially  the 
same  thing,'  or  'practically  the  same,  as  the  thesis 
maintained.'  Thus  one  might  take  the  fact  that  a  great 
many  people  are  not  regular  church-goers,  as  a  proof 
of  the  proposition  that  religion  and  morality  are  dying 
out  in  the  country.  Many  of  the  arguments  brought 
against  scientific  and  philosophical  theories  belong  to 
this  class.  Mill  cites  the  arguments  which  have  been 
urged  against  the  Malthusian  doctrine  of  population, 
and  Berkeley's  theory  of  matter.  We  may  quote  the 


1 68  FALLACIES   OF  DEDUCTIVE   REASONING 

passage  referring  to  the  former :  "  Malthus  has  been 
supposed  to  be  refuted  if  it  could  be  shown  that  in 
some  countries  or  ages  population  has  been  nearly 
stationary,  as  if  he  had  asserted  that  population  always 
increases  in  a  given  ratio,  or  had  not  expressly  declared 
that  it  increases  only,  in  so  far  as  it  is  not  restrained  by 
prudence,  or  kept  down  by  disease.  Or,  perhaps,  a 
collection  of  facts  is  produced  to  prove  that  in  some  one 
country  with  a  dense  population  the  people  are  better 
off  than  they  are  in  another  country  with  a  thin  one,  or 
that  the  people  have  become  better  off  and  more 
numerous  at  the  same  time ;  as  if  the  assertion  were 
that  a  dense  population  could  not  possibly  be  well  off."  1 

There  are  several  cases  or  forms  of  Irrelevant  Con- 
clusion to  which  special  names  have  been  given,  and 
which  it  is  important  to  consider  separately.  When 
an  argument  bears  upon  the  real  point  at  issue,  it  is 
called  argumentum  ad  rem.  But,  on  the  other  hand, 
there  are  the  following  special  ways  of  obscuring  the 
issue :  —  argumentum  ad  hominem,  argumentum  ad  popu- 
lum,  argumentum  ad  ignorantiam,  and  argumentum  ad 
verecundiam. 

The  argumentum  ad  hominem  is  an  appeal  to  the 
character,  principles,  or  former  profession  of  the  person 
against  whom  it  is  directed.  It  has  reference  to  a 
person  or  persons,  not  to  the  real  matter  under  discus- 
sion. In  order  to  confuse  an  opponent,  and  discredit 
him  with  the  audience,  one  may  show  that  his  character 
is  bad,  or  that  the  views  which  he  is  now  maintaining 

^  Logic,  Bk.  V.  Ch.  VII.  §3. 


§46.     MATERIAL   FALLACIES  169 

are  inconsistent  with  his  former  professions  and  practice. 
Or  the  argument  may  be  used  with  the  hope  of  persuad- 
ing the  opponent  himself.  We  then  try  to  convince 
him  that  the  position  which  he  maintains  is  inconsistent 
with  some  other  view  which  he  has  previously  pro- 
fessed, or  with  the  principles  of  some  sect  or  party 
which  he  has  approved.  Or  we  may  appeal  to  his  in- 
terests by  showing  him  that  the  action  proposed  will 
affect  injuriously  some  cause  in  which  he  is  concerned, 
or  will  benefit  some  rival  sect  or  party.  In  all  of  these 
cases  the  real  point  at  issue  is,  of  course,  evaded. 

The  argumetvtiim  ad  populum  is  an  argument  ad- 
dressed to  the  feelings,  passions,  and  prejudices  of 
people  rather  than  an  unbiassed  discussion  addressed  to 
the  intellect. 

The  argumentum  ad  ignorantiam  is  an  attempt  to 
gain  support  for  some  position  by  dwelling  upon  the 
impossibility  of  proving  the  opposite.  Thus  we  cannot 
prove  affirmatively  that  spirits  do  not  revisit  the  earth, 
or  send  messages  to  former  friends  through  'mediums,' 
Now  it  is  not  unusual  to  find  ignorance  on  this  subject 
advanced  as  a  positive  ground  of  conviction.  The 
argument  seems  to  be  :  — 

It  is  not  impossible  that  this  is  so, 
What  is  not  impossible  is  possible, 
Therefore  it  is  possible  that  this  is  so. 

The  fallacy  arises  when  we  confuse  what  is  only  ab- 
stractly possible  —  i.e.,  what  we  cannot  prove  to  be 
impossible  —  with  what  is  really  possible,  i.e.,  with  what 
we  have  some  positive  grounds  for  believing  in,  though 
those  grounds  are  not  sufficient  to  produce  conviction. 


I/O  'FALLACIES   OF  DEDUCTIVE   REASONING 

The  argumentum  ad  verecundiam  is  an  appeal  to  the 
reverence  which  most  people  feel  for  a  great  name. 
This  method  of  reasoning  attempts  to  settle  a  question 
by  referring  to  the  opinion  of  some  acknowledged 
authority,  without  any  consideration  of  the  arguments 
which  are  advanced  for  or  against  the  position.  It  is,  of 
course,  right  to  attach  much  importance  to  the  views  of 
great  men,  but  we  must  not  suppose  that  their  opinion 
amounts  to  proof,  or  forbids  us  to  consider  the  matter 
for  ourselves. 

There  is,  however,  a  more  common,  though  still  less 
justifiable,  form  of  the  argument  from  authority.  A 
man  who  is  distinguished  for  his  knowledge  and  attain- 
ments in  some  particular  field,  is  often  quoted  as  an 
authority  upon  questions  with  which  he  has  no  special 
acquaintance.  The  prestige  of  a  great  name  is  thus 
irrelevantly  invoked  when  no  significance  properly 
attaches  to  it.  Thus,  for  example,  a  successful  general 
is  supposed  to  speak  with  authority  upon  problems  of 
statescraft,  and  the  opinions  of  prominent  clergymen 
are  quoted  regarding  the  latest  scientific  theories. 

(4)  The  fallacy  of  non  sequitur,  or  the  fallacy  of  the 
consequent,  occurs  when  the  conclusion  does  not  really 
follow  from  the  premises  by  which  it  is  supposed  to  be 
supported.  The  following  example  may  serve  as  an 
illustration :  — 

Pennsylvania  contains  rich  coal  and  iron  mines, 
Pennsylvania  has  no  sea-coast, 

Therefore  the  battle  of  Gettysburg  was  fought  in  that  state. 
This  argument,  of  course,  is  thoroughly  inconsequent, 


§46.     MATERIAL   FALLACIES  I /I 

and  would  deceive  no  one.  But  when  the  conclusion 
repeats  some  words  or  phrases  from  the  premises,  we 
are  likely,  when  not  paying  close  attention,  to  be  im- 
posed upon  by  the  mere  form  of  the  argument.  We 
notice  the  premises,  and  remark  that  the  person  using 
the  argument  advances  boldly  through  '  therefore  '  to  his 
conclusion.  And  if  this  conclusion  appears  to  .be  related 
to  the  premises,  and  sounds  reasonable,  the  argument  is 
likely  to  be  accepted.  The  following  example  will  illus- 
trate this :  — 

Every  one  desires  happiness,  and  virtuous  people  are  happy, 
Therefore  every  one  desires  to  be  virtuous. 

What  is  known  as  the  False  Cause  (non  causa  pro 
causa  ;  post  hoc  ergo  propter  hoc)  is  the  inductive  fallacy 
corresponding  to  the  non  sequitur.  In  this  we  assume 
that  one  thing  is  the  cause  of  another  merely  because  we 
have  known  them  to  happen  together  a  number  of  times. 
The  causal  relation  is  assumed  without  any  analysis  or 
examination,  on  the  ground  of  some  chance  coincidence. 
Thus  a  change  in  the  weather  may  be  attributed  to  the 
moon,  or  the  prosperity  of  the  country  to  its  laws  re- 
quiring Sunday  observance  (cf.  pp.  255  f.). 

References 

J.  H.  Hyslop,  The  Elements  of  Logic,  Chs.  XVII.  and  XVIII. 

J.  S.  Mill,  Logic,  Bk.  V. 

A.  Sidgwick,  Fallacies  [Int.  Scient.  Series]. 


PART    II.— INDUCTIVE    METHODS 


CHAPTER   XIII 

THE    PROBLEM    OF    INDUCTION.       OBSERVATION    AND 
EXPLANATION 

§  47.  The  Problem  of  Induction.  —  In  Part  I.  we  have 
outlined  the  general  nature  of  the  syllogism,  and  have 
shown  what  conditions  must  be  fulfilled  in  order  to 
derive  valid  conclusions  from  given  premises.  But  the 
syllogism  does  not  represent  completely  all  of  our  ways  of 
thinking.  We  do  not  always  find  premises  which  every 
one  accepts  ready  to  our  hand.  The  propositions  which 
serve  as  the  premises  of  syllogisms  are  themselves  the 
result  of  the  activity  of  thought.  It  requires  thinking 
to  arrive  at  such  simple  propositions  as,  '  all  men  are 
mortal/  'water  is  composed  of  hydrogen  and  oxygen.' 
Facts  of  this  kind  are  of  course  learned  through  expe- 
rience, but  they  none  the  less  require  thought  for  their 
discovery.  Sense-perception  without  thought  could  give 
us  only  a  chaos  of  unordered  impressions  which  would 
have  no  meaning  and  no  significance.  It  is  important, 
then,  to  understand  how  our  intelligence  proceeds  to 
discover  the  real  nature  of  things,  and  the  laws  accord- 
ing to  which  they  operate.  Thinking  is  the  means  by 
which  we  interpret  nature,  and  to  show  how  this  is  to 

172 


§47-    THE   PROBLEM   OF  INDUCTION  173 

be  accomplished  was  the  purpose  of  Bacon's  Novum  Or- 
ganum.  The  problem  is  the  discovery  of  the  real  nature 
of  things,  and  their  relations  with  one  another.  The 
assumption  of  all  knowledge,  as  we  have  already  seen 
(§  9,  cf.  also  §§  79,  80),  is  that  there  is  a  permanent  con- 
stitution of  things  which  secures  uniform  ways  of  acting. 
The  procedure  by  means  of  which  intelligence  discovers 
the  permanent  laws  of  things  is  usually  known  as  In- 
duction. We  shall  have  to  study  this  kind  of  thinking 
in  this  and  the  following  chapters.  The  general  prob- 
lem may  perhaps  be  stated  in  this  way :  What  are  the 
methods  which  inductive  thinking  employs,  in  order  to 
pass  from  the  chaotic  and  unordered  form  in  which  the 
senses  present  our  experience,  to  a  perception  of  the 
order  and  law  in  things  that  is  required  by  real  know- 
ledge or  science  ? 

Before  we  attempt  to  answer  this  question,  however, 
there  are  several  remarks  to  be  made  which  will,  I 
hope,  throw  further  light  upon  the  nature  of  our  under- 
taking. In  the  first  place,  it  is  to  be  noticed  that  we 
have  spoken  in  the  preceding  paragraph  of  the  methods 
of  inductive  thinking.  Now,  as  we  shall  show  more 
fully  in  §  88,  there  is  no  essential  difference  between 
the  results  of  an  inductive  and  a  deductive  inference. 
The  purpose  of  an  inference  is  always  the  same : 
namely,  to  exhibit  the  relation  and  connection  of  par- 
ticular facts  or  events  in  virtue  of  some  universal  law 
or  principle.  In  deductive  thinking,  such  a  law  is 
known,  or  provisionally  assumed  as  known,  and  the 
problem  is  •  to  show  its  application  to  the  facts  with 
which  we  are  dealing.  In  induction,  on  the  other  hand, 


1/4  THE  PROBLEM  OF  INDUCTION 

the  starting-point  must  be  the  particular  facts,  and  the 
task  which  thought  has  to  perform  is  to  discover  the 
general  law  of  their  connection.  Both  deduction  and 
induction  play  an  important  part  in  the  work  of  building 
up  knowledge.  But  the  various  sciences  must  start 
with  particular  facts  learned  through  experience.  The 
mind  has  not  before  experience  any  store  of  general 
principles  or  innate  truths  which  might  serve  as  the 
starting-point  of  knowledge  (cf.  §  76).  It  must  fall 
back,  therefore,  upon  the  particular  facts  and  events 
learned  through  perception.  This  'elementary  know- 
ledge,' as  has  been  already  pointed  out,  does  not  pass 
over  in  a  ready-made  form  into  the  mind,  but  is  itself 
the  result  of  thinking  or  judging.  However,  before 
any  one  deliberately  and  consciously  undertakes  to  dis- 
cover new  truth,  to  understand  the  world,  he  is  already 
in  possession  of  a  store  of  such  perceptive  judgments. 
These  constitute  the  beginnings  of  knowledge,  and 
serve  as  the  starting-point  for  scientific  explanation. 
The  knowledge  of  laws  and  general  principles  comes 
later,  and  is  derived  from  a  study  of  the  particular  facts. 
It  is  clear,  then,  that  the  procedure  of  all  the  sciences 
must  be  inductive,  at  least  in  the  beginning.  The  various 
sciences  are  occupied,  each  in  its  particular  field,  with 
an  attempt  to  reduce  to  order  and  unity  facts,  which  at 
first  sight  appear  to  be  lawless  and  disconnected.  And 
it  is  true  to  say  that  in  this  undertaking  the  general 
procedure  is  inductive.  But  it  will  also  appear  that  in 
performing  this  task  thought  does  not  always  proceed 
in  strictly  inductive  fashion.  Our  thought  uses  every 
means  which  will  help  it  to  its  desired  end.  It  is  often 


§47-     THE   PROBLEM   OF  INDUCTION  175 

able,  after  pushing  its  inquiries  a  little  way,  to  discover 
some  general  principle,  or  to  guess  what  the  law  of 
connection  must  be.  When  this  is  possible,  it  is  found 
profitable  to  proceed  deductively,  and  to  show  what  re- 
sults necessarily  follow  from  the  truth  of  such  a  general 
law.  Of  course,  it  is  always  essential  to  verify  results 
obtained  in  this  deductive  way,  by  comparing  them  with 
the  actual  facts.  But  in  general,  the  best  results  are 
obtained  when  induction  and  deduction  go  hand  in 
hand.  We  shall  expect  to  find,  then,  that  the  so-called 
inductive  methods  sometimes  include  steps  which  are 
really  deductive  in  nature. 

It  is  to  be  noticed,  further,  that  in  dealing  with  the  nature  of  the 
inductive  methods,  we  are  not  laying  down  rules  which  thought  must 
follow.  We  are  not  attempting,  that  is,  to  prescribe  to  thinking  its 
mode  of  procedure.  To  do  so  would  be  quite  futile.  It  is  impos- 
sible, as  we  have  already  seen  (§  3),  for  logic  to  lay  down  any 
a  priori  rules.  Its  task  is  rather  to  point  out  the  methods  by  which 
success  has  been  already  won  in  the  various  fields  of  knowledge. 
Logic  does  not  attempt  to  invent  any  methods  of  scientific  proced- 
ure, but  it  undertakes  to  describe  the  road  by  which  truth  has 
already  been  gained.  The  scientific  inquirer  is  interested  pri- 
marily in  the  results  of  his  thinking :  he  is  usually  not  interested  in 
tracing  the  various  steps  through  which  his  thought  has  passed,  and 
the  methods  employed  in  reaching  the  goal.  Oftentimes  he  would 
be  unable  to  give  any  such  description  even  if  he  tried  to  do  so. 
Logic,  however,  takes  the  procedure  of  the  thinking  process  for  its 
subject-matter.  It  undertakes  to  make  thought  conscious  of  its 
own  nature,  of  the  goal  at  which  it  aims,  and  the  methods  which 
are  employed  in  the  attainment  of  this  goal.  The  comparative 
value  of  these  methods,  too,  must  be  decided  by  the  actual  charac- 
ter of  the  results  which  they  have  yielded.  One  method  is  to  be 
regarded  as  better  than  another  when  it  gives  us  knowledge  which 
is  universally  acknowledged  to  be  more  complete  and  satisfactory 


1/6  THE  PROBLEM   OF  INDUCTION 

than  that  afforded  by  the  other.     For  logical  methods,  like  every- 
thing else,  must  be  known  and  judged  by  their  fruits. 

Again,  it  must  be  remembered  that  complete  scien- 
tific explanation,  which  we  found  to  be  the  type  of  per- 
fect knowledge,  is  not  attained  at  a  single  stroke. 
Scientific  inquiry  may  have  various  purposes.  It  is 
often  limited  to  an  attempt  to  gain  a  knowledge  of  the 
quantitative  relations  of  things,  or  of  the  way  in  which 
they  are  connected  as  antecedents  and  consequents. 
In  some  cases,  too,  the  conclusions  reached  are  only 
more  or  less  probable,  and  require  further  confirmation 
through  the  use  of  other  methods.  It  follows,  then, 
that  the  various  scientific  methods  which  we  shall  have 
to  describe  are  not  to  be  regarded  as  self-sufficient  and 
independent  ways  of  reaching  truth,  but  rather  as 
mutually  helpful  and  complementary.  For  example,  the 
work  done  by  thought  in  dealing  with  the  quantitative 
aspect  of  things,  and  the  conclusions  which  it  reaches 
through  analogical  inference,  are  necessary  steps  in  the 
progress  toward  complete  and  satisfactory  explanations 
of  the  nature  of  things.  We  shall  find  it  necessary,  there- 
fore, to  keep  in  mind  in  our  investigation  this  relation 
of  the  various  methods  to  one  another.  For  our  purpose, 
we  may  perhaps  classify  the  various  scientific  methods 
as  those  of  Observation  and  Explanation,  the  latter  in- 
cluding Analogy  and  Complete  Scientific  Explanation. 

§  48.  Observation.  —  We  may  include  under  this 
heading,  Simple  Enumeration,  Statistical  Methods,  and 
Methods  of  determining  Causal  Connection.  Before 
describing  these  processes  in  detail,  however,  it  is  neces- 


§48.     OBSERVATION  177 

sary  to  make  clear  what  is  implied  in  the  nature  of  scien- 
tific observation,  and  what  are  the  results  aimed  at  by  the 
methods  which  it  employs.  It  is  customary  to  say  that 
Observation  has  to  determine  the  nature  and  order  of  the 
particular  facts  presented  by  our  experience,  and  that 
after  this  has  been  done,  there  still  remains  the  task  of 
furnishing  the  theory,  or  Explanation  of  the  facts.  This 
distinction,  though  not  absolute,  affords  a  convenient 
principle  of  division  in  treating  of  the  inductive  methods. 
We  may  say  that  it  is  observation  which  enables  us  to 
discover  the  nature  of  particular  facts,  and  to  determine 
the  order  of  their  connection.  Accurate  observation  is 
thus  a  first  and  necessary  step  in  the  work  of  reducing 
our  experience  to  systematic  form.  We  have  already 
seen  how  emphatically  and  eloquently  this  doctrine  was 
proclaimed  by  Bacon  in  the  Novum  Organum. 

It  is  important,  however,  to  remember  that  scientific 
observation  itself  involves  intellectual  activity.  To 
observe  —  at  least  in  the  sense  in  which  the  word  is 
used  in  scientific  procedure  —  requires  something  more 
than  the  passive  reception  of  impressions  of  sense  in 
the  order  in  which  they  come  to  us.  Without  some 
activity  on  the  part  of  mind,  it  would  be  impossible  to 
obtain  even  the  imperfect  and  fragmentary  knowledge 
of  everyday  life.  But  accurate  observation  is  one  of 
the  means  which  science  employs  to  render  this  know- 
ledge more  complete  and  satisfactory ;  and  when  obser- 
vation thus  becomes  an  exact  and  conscious  instrument, 
it  involves,  to  even  a  greater  extent  than  in  ordinary 
life,  intellectual  activities  like  judgment  and  inference. 
It  is  because  this  is  true,  because  scientific  observation 


178  THE   PROBLEM   OF   INDUCTION 

demands  the  constant  exercise  of  thought,  in  selecting 
and  comparing  the  various  elements  in  the  material 
with  which  it  deals,  that  it  affords  such  excellent  intel- 
lectual discipline.  The  observational  sciences  do  not 
merely  train  the  sense-organs;  the  discipline  which 
they  afford  is  mental  as  well  as  physiological,  and  it 
is,  of  course,  true  that  mental  training  can  only  be 
gained  through  the  exercise  of  mental  activity. 

It  is  quite  true  that  it  is  of  the  utmost  importance  to  distinguish 
between  a  fact,  and  further  inferences  from  the  fact.  As  will  be 
pointed  out  in  the  chapter  on  Inductive  Fallacies,  errors  very  fre- 
quently arise  from  confusing  facts  and  inferences.  The  point  which 
is  emphasized  in  the  previous  paragraph,  however,  is  that  it  requires 
a  certain  amount  of  thinking  in  order  to  get  a  fact  at  all.  Facts  do 
not  pass  over  ready-made  into  the  mind.  Sirriply  to  stare  at  things 
does  not  give  us  knowledge  ;  unless  our  mind  reacts,  judges,  thinks, 
we  are  not  a  bit  the  wiser  for  staring.  To  observe  well,  it  is  neces- 
sary to  be  more  or  less  definitely  conscious  of  what  one  is  looking 
for,  to  direct  one's  attention  towards  some  particular  field  or  object ; 
and  to  do  this  implies  selection  among  the  multitude  of  impressions 
and  objects  of  which  we  are  conscious.  Moreover,  scientific  obser- 
vation requires  analysis  and  discrimination.  It  is  not  unusual,  in 
text-books  on  logic,  to  symbolize  the  various  facts  learned  through 
observation  by  means  of  letters,  #,  b,  c,  etc.,  and  to  take  it  for  granted 
that  they  are  given  in  our  experience  as  distinct  and  separate  phe- 
nomena ;  but,  as  we  have  just  seen,  judgments  of  analysis  and 
discrimination  are  necessary  to  separate  out  the  so-called  '  phenom- 
ena' from  the  mass  or  tangle  of  experience  in  which  they  were 
originally  given.  Again,  to  determine  the  nature  of  a  fact  through 
observation,  it  is  essential  to  note  carefully  how  it  differs  from 
other  facts  with  which  it  is  likely  to  be  confused,  and  also,  to  some 
extent,  what  relations  and  resemblances  it  has.  But  such  knowledge 
presupposes  that  thought  has  already  been  at  work  in  forming  judg- 
ments of  comparison. 


§48.     OBSERVATION  179 

It  may  seem  strange  at  first  sight  that  the  determina- 
tion of  the  causal  order  and  connection  of  phenomena 
should  be  regarded  as  belonging  to  Observation  rather 
than  to  Explanation.  To  discover  the  causes  of  things 
is,  indeed,  a  very  essential  step  in  the  process  of  expla- 
nation; but,  as  will  appear  more  fully  hereafter,  the 
distinction  between  observation  and  explanation  is  not 
an  absolute  one.  The  process  of  knowledge  is  essen- 
tially the  same  from  beginning  to  end.  The  determina- 
tion of  the  nature  and  order  of  phenomena  is  a  long 
step  towards  rendering  them  comprehensible.  If  the 
distinction  between  observation  and  explanation  as 
methods  of  scientific  procedure  is  to  be  made,  it  seems 
right  to  assign  to  observation  the  task  of  determining 
what  phenomena  are  invariably  conjoined  as  antecedents 
and  consequents.  Experience  presents  to  us  a  variety 
of  objects  simultaneously  or  in  rapid  succession,  but 
in  many  cases  such  conjunction  is  merely  temporary 
and  accidental.  The  problem  which  scientific  obser- 
vation has  here  to  determine  is  the  discovery  of  what 
particular  phenomena  are  necessarily  connected,  what  are 
the  real  antecedents  and  consequents  in  the  case.  '  The 
sun  was  very  hot  this  morning,  and  a  picnic  party  went 
on  the  lake,  and  this  afternoon  there  is  a  severe  thunder- 
storm.' These  events  (and  many  others)  are  conjoined 
temporally.  Is  there  also  a  real  connection  between 
any  of  them,  or  is  their  concurrence  merely  accidental  ? 
This  is  the  question  which  must  be  answered  by  the 
methods  of  determining  causal  connection.  ,  Of  course 
merely  passive  observation  will  not  suffice  to  obtain  an 
answer.  The  relation  of  antecedent  and  consequent  is 


180  THE   PROBLEM   OF   INDUCTION 

not  given,  but  has  to  be  made  out  by  the  help  of  analysis 
and  inference.  But,  since  the  point  to  be  determined 
has  reference  to  the  nature  and  order  of  a  set  of  facts 
which  can  be  observed,  the  methods  employed  may  well 
be  included  under  Observation. 

A  distinction  is  sometimes  made  between  observa- 
tion and  experiment.  In  observation,  it  is  said,  the 
mind  simply  finds  its  results  presented  to  it  in  nature, 
while  in  experiment  the  answer  to  a  question  is  obtained 
by  actively  controlling  and  arranging  the  circumstances 
at  will.  There  are,  no  doubt,  some  grounds  for  this  dis- 
tinction, though  it  is  not  true  that  the  mind  is  passive 
in  the  one  case,  and  active  in  the  other.  Even  in  ob- 
servation, as  we  have  seen,  knowledge  always  arises 
through  active  analysis  and  comparison  of  the  impres- 
sions received  through  sense.  The  difference  is  rather 
this :  In  observing,  where  experiment  is  impossible,  one 
must  wait  for  events  to  occur,  and  must  take  them  in 
the  order  in  which  they  are  presented  in  the  natural 
series.  But,  where  experiment  is  employed,  we  have 
control  of  the  conditions,  and  can  produce  the  phe- 
nomena to  be  investigated  in  any  order,  and  as  often 
as  we  choose.  In  experiment,  as  Bacon  says,  we  can 
put  definite  questions  to  nature,  and  compel  her  to 
answer.  This  is,  of  course,  an  immense  advantage. 
In  some  of  the  sciences,  however  —  geology  and  as- 
tronomy for  example  —  it  is  not  possible  thus  to  con- 
trol the  conditions :  one  must  wait  and  observe  the 
results  of  nature's  experiments.  Physics  and  chemis- 
try are  the  experimental  sciences  par  excellence ;  and, 
in  general,  we  may  say  that  a  science  always  makes 


§48.     OBSERVATION  l8l 

more  rapid  progress  when  it  is  found  possible  to  call 
experiment  to  the  aid  of  observation.  It  is  not  possible 
to  conceive  how  physics  and  chemistry  could  have 
reached  their  present  state  of  perfection  without  the 
assistance  of  experiment.  Indeed,  the  almost  total 
neglect  of  experiment  by  the  Greek  and  mediaeval 
scholars  must  be  regarded  as  one  of  the  chief  reasons 
why  the  physical  sciences  made  so  little  progress  dur- 
ing those  centuries.  Dr.  Fowler  states  in  the  following 
passage  some  of  the  main  advantages  to  be  derived 
from  experiment :  — 

"To  be  able  to  vary  the  circumstances  as  we  choose,  to  produce 
the 'phenomenon  under  investigation  in  the  precise  degree  which  is 
most  convenient  to  us,  and  as  frequently  as  we  wish,  to  combine  it 
with  other  phenomena  or  to  isolate  it  altogether,  are  such  obvious 
advantages  that  it  is  not  necessary  to  insist  upon  them.  Without 
the  aid  of  artificial  experiment  it  would  have  been  impossible,  for 
instance,  to  ascertain  the  laws  of  falling  bodies.  To  disprove  the 
old  theory  that  bodies  fall  in  times  inversely  proportioned  to  their 
weight,  it  was  necessary  to  try  the  experiment ;  to  be  able  to  affirm 
with  certainty  that  all  bodies,  if  moving  in  a  non-resisting  medium, 
would  fall  to  the  earth  through  equal  vertical  spaces  in  equal  times, 
it  was  essential  to  possess  the  means  of  removing  altogether  the 
resisting  medium  by  some  such  contrivance  as  that  of  the  air-pump. 
.  .  .  Even  when  observation  alone  reveals  to  us  a  fact  of  nature, 
experiment  is  often  necessary  in  order  to  give  precision  to  our 
knowledge.  That  the  metals  are  fusible,  and  that  some  are  fusible 
at  a  lower  temperature  than  others,  is  a  fact  which  we  can  conceive 
to  have  been  obtruded  upon  man's  observation,  but  the  precise 
temperature  at  which  each  metal  begins  to  change  the  solid  for  the 
liquid  condition  could  be  learned  only  by  artificial  experiment." 1 

It  is  important,  then,  to  recognize  the  services  which 

1  Fowler,  Inductive  Logic,  p.  41  f. 


1 82  THE   PROBLEM   OF   INDUCTION 

experiment  renders  in  helping  us  to  understand  the 
facts  with  which  the  various  sciences  deal.  But  it  is  not 
necessary  to  distinguish  experiment  from  observation  as 
if  it  were  a  separate  and  independent  mode  of  investiga- 
tion. We  should  rather  say  that  observation,  in  the 
sense  in  which  we  have  used  the  word,  employs  experi- 
ment wherever  practicable  as  an  indispensable  auxiliary. 
The  methods  of  observation,  then,  which  have  still  to  be 
described,  will  in  many  cases  call  for  the  employment  of 
experiments.  Indeed,  it  will  be  seen  that  some  of  these 
are  essentially  methods  of  experimentation. 

§  49.  Explanation.  —  We  have  already  seen  that  the 
distinction  between  observation  and  explanation  is  not 
an  absolute  one.  The  task  which  thought  has  to  per- 
form —  the  task  which  is  undertaken  by  science  —  is  to 
reduce  the  isolated  and  chaotic  experiences  of  ordinary 
life  to  order  and  system.  And  it  is  important  to  remem- 
ber that  all  the  various  methods  employed  contribute 
directly  towards  that  result.  It  has,  however,  seemed 
possible  to  divide  this  undertaking  into  two  main  divis- 
ions. Observation,  it  was  said,  seeks  to  discover  the 
exact  nature  of  the  facts  to  be  dealt  with,  and  also  to 
determine  the  ways  in  which  they  are  necessarily  and 
invariably  connected.  But,  when  this  has  been  accom- 
plished, we  have  not  by  any  means  reached  an  end  of 
the  matter.  The  desire  for  knowledge  is  not  satisfied 
with  a  mere  statement  of  facts,  or  with  the  information 
that  certain  phenomena  always  occur  in  a  fixed  order 
as  antecedents  and  consequents.  Complete  knowledge 
demands  an  explanation  of  the  facts  as  thus  determined 


§49-     EXPLANATION  183 

by  the  methods  of  observation.  '  Why?  we  ask, '  should  a 
always  precede  b  ? '  '  Why  should  dew  be  deposited  under 
such  and  such  conditions,  or  water  rise  thirty-two  feet  in 
a  pump  ? '  Science,  we  feel,  should  do  more  than  de- 
scribe the  facts ;  it  should  offer  an  explanation  of 
them  as  well.  To  explain  events,  however,  is  to  furnish 
reasons  for  them.  The  scientist  is  not  content  to  know 
merely  that  such  and  such  phenomena  exist,  and  occur 
in  conjunction  with  each  other,  but  he  attempts  to  dis- 
cover why  this  is  so.  His  knowledge  is  not  confined  to 
the  '  what,'  but  includes  the  '  why.'  It  is,  of  course,  true 
that  a  large  part  of  scientific  work  is  occupied  with  an 
attempt  to  determine  precisely  and  accurately  the  nature 
of  facts.  Until  the  facts  are  thus  scientifically  deter- 
mined attempts  at  explanation  are  usually  quite  futile. 
But  after  this  has  been  accomplished,  it  is  still  necessary 
to  show  reasons  why  the  phenomena  with  which  we  are 
dealing  have  the  precise  character  which  they  are  found 
to  possess,  and  why  they  should  occur  in  the  invariable 
order  in  which  they  are  observed.  Explanation,  in  other 
words,  completes  the  knowledge  obtained  through  ob- 
servation. It  does  further  intellectual  work  on  the 
results  given  by  the  latter  process.  Explanation,  itself, 
has  various  degrees  of  completeness  ;  it  may  be  more  or 
less  satisfactory.  When  we  come  to  treat  Analogy,  for 
example,  we  shall  find  that  it  affords  a  kind  of  expla- 
nation, though  not  one  of  an  entirely  satisfactory 
type.  In  general,  however,  we  may  say  that  explana- 
tion goes  beyond  the  particular  facts,  and  seizes  upon 
general  principles  or  laws  to  which  the  facts  are  re- 
ferred. And  it  is  only  when  one  knows  the  general  law 


184  THE   PROBLEM   OF  INDUCTION 

or  principle  involved  in  the  case,  that  one  can  be  said 
really  to  understand  the  particular  facts. 

It  is  usually  said  that  where  we  know  merely  the  nature  of  phe- 
nomena, and  their  connection,  without  being  able  to  explain  these 
facts,  our  knowledge  is  empirical.  Thus,  I  may  know  that  an  ex- 
plosion follows  the  contact  of  a  lighted  match  with  gunpowder,  or 
that  a  storm  follows  when  there  is  a  circle  around  the  moon,  without 
being  able  to  explain  in  any  way  why  these  facts  are  connected. 
On  the  other  hand,  if  We  can  connect  events  by  showing  the  gen- 
eral principle  involved,  we  say  that  our  knowledge  is  really  scientific. 
It  is  important  to  notice,  however,  that  empirical  knowledge  is  simply 
in  a  less  advanced  stage  than  the  scientific  knowledge  which  has  suc- 
ceeded in  gaining  an  insight  into  the  general  law.  Empirical  know- 
ledge leaves  a  problem  which  intelligence  has  still  to  solve.  It  is,  of 
course,  true  that  a  large  part  of  every  one's  knowledge  is  empirical  in 
character.  We  all  know  many  things  which  we  cannot  explain.  In 
all  the  sciences,  too,  phenomena  are  met  with  which  seem  to  defy  all 
attempts  at  explanation.  Indeed,  some  of  the  sciences  can  scarcely 
be  said  tc  have  passed  the  empirical  stage.  The  science  of  medi- 
cine, for  example,  has  hardly  yet  reached  any  knowledge  of  general 
principles.  The  physician  knows,  that  is,  as  a  result  of  actual  ex- 
periment, that  such  and  such  drugs  produce  such  and  such  effects. 
But  he  knows  almost  nothing  of  the  means  by  which  this  result  is 
achieved,  and  is  therefore  unable  to  go  beyond  the  fact  itself.  In 
this  respect,  he  is  very  little  better  off  than  the  ordinary  man,  who 
knows  that  if  he  eats  certain  kinds  of  food  he  will  be  ill,  or  if  he 
drinks  strong  liquors  in  excess  he  will  become  intoxicated. 


CHAPTER    XIV 

METHODS    OF    OBSERVATION. ENUMERATION    AND    STA- 
TISTICS 

§  50.  Enumeration  or  Simple  Counting.  —  We  shall 
begin  the  account  of  the  scientific  methods  with  Enu- 
meration. To  count  the  objects  which  we  observe, 
and  to  distinguish  and  number  their  parts,  is  one  of 
the  first  and  most  essential  operations  of  thought.  It  is 
of  course  true  that  qualitative  distinctions  precede  quan- 
titative. The  child  learns  to  distinguish  things  by  some 
qualitative  mark,  such  as  'black'  or  'hot,'  before  he  is 
able  to  count  them  (cf.  §  82).  But  we  may  say,  never- 
theless, that  the  qualities  of  things  are  known,  in  a 
general  way  at  least,  before  scientific  procedure  begins. 
The  determination  of  quantity,  on  the  other  hand,  seems 
to  demand  a  more  conscious  effort  on  the  part  of  the 
mind.  We  learn,  that  is,  to  distinguish  the  general 
qualities  of  things  without  effort,  but,  in  order  to  obtain 
quantitative  knowledge,  it  is  necessary  to  set  ourselves 
deliberately  to  work.  We  may,  therefore,  take  Enumer- 
ation, or  Simple  Counting,  which  is  perhaps  the  easiest 
kind  of  quantitative  determination,  as  our  starting-point 
in  dealing  with  the  Inductive  Methods. 

A  considerable  step  in  advance,  in  the  task  of  re- 
ducing the  world  of  our  experience  to  order  and  unity, 
is  taken  when  we  begin  to  count,  i.e.,  to  group  together 

185 


1 86  ENUMERATION   AND   STATISTICS 

things  of  the  same  kind,  and  to  register  their  number. 
Thus  Enumeration  is,  to  some  extent,  also  a  process  of 
classification.  What  is  counted  is  always  a  collective 
whole,  the  units  of  which  are  either  all  of  the  same  kind, 
or  else  belong  to  a  limited  number  of  different  classes. 
Thus  one  might  determine  by  Enumeration  the  number 
of  sheep  in  a  flock,  taking  each  individual  as  belonging 
to  the  same  general  class,  '  sheep ' ;  or  the  analysis  might 
be  pushed  further  so  as  to  give  as  a  result  the  number 
of  white  and  of  black  sheep  separately.  The  purpose 
for  which  the  enumeration  is  undertaken  always  deter- 
mines the  length  to  which  the  process  of  analysis  and 
distinction  is  carried.  For  example,  if  the  object  of  a 
census  enumeration  were  simply  to  determine  the  num- 
ber of  inhabitants  in  a  country,  it  would  not  be  neces- 
sary to  make  any  distinctions,  but  each  person  would 
count  as  one.  But  where,  as  is  often  the  case,  the 
aim  is  not  simply  to  count  the  sum-total,  but  also  to  de- 
termine the  relative  numbers  belonging  to  various 
classes,  analysis  has  to  be  pushed  further.  In  such 
cases,  we  might  count  the  number  belonging  to  each 
sex,  the  native-born,  and  those  of  foreign  birth,  those 
below,  and  those  above  any  given  age,  etc. 

It  will  be  noticed  that  the  process  of  enumeration 
takes  account  of  each  individual  instance.  And  the 
judgment  which  sums  up  the  process  puts  the  result  in 
a  numerical  form.  'There  are  twenty-five  thousand 
inhabitants  in  this  town,  five  thousand  of  whom  are  of 
foreign  birth.'  In  cases  where  the  examination  of  par- 
ticular instances  has  been  exhaustive,  the  result  may  be 
stated  in  the  form  of  a  universal  proposition.  Thus, 


§50.     ENUMERATION   OR   SIMPLE  COUNTING         l8/ 

after  examining  the  calendar  of  each  of  the  months 
separately,  we  might  say :  '  All  of  the  months  contain 
less  than  thirty- two  days.'  Or,  after  measuring  each 
individual  in  a  company,  the  assertion  might  be  made : 
'No  one  in  this  company  is  more  than  six  feet  tall.' 
Cases  of  this  kind,  where  a  general  assertion  is  made 
after  an  examination  of  all  the  individuals  concerned, 
are  termed  by  Jevons,  instances  of  Perfect  Induction. 
"  An  Induction,  that  is  an  act  of  Inductive  reasoning,  is 
called  Perfect,  when  all  the  possible  cases  or  instances 
to  which  the  conclusion  can  refer,  have  been  examined 
and  enumerated  in  the  premises."  l  On  the  other  hand, 
where,  as  usually  happens,  it  is  impossible  to  examine 
all  the  cases,  the  inductive  process  is  regarded  as  Im- 
perfect by  the  same  writer,  and  the  conclusion  expressed 
in  the  general  law  as  only  probable.  The  assertion 
that  all  the  months  of  the  year  contain  less  than  thirty- 
two  days,  is  derived  from  Perfect  Induction,  and  is  ab- 
solutely certain,  but  the  proposition  that  'all  men  are 
mortal,'  is  derived  from  Imperfect  Induction,  and  there 
is  no  certainty,  but  only  a  probability  that  all  future 
cases  will  agree  with  those  which  we  have  already 
experienced. 

This  distinction,  however,  seems  to  be  founded  on  a 
mistaken  view  of  the  nature  of  inductive  reasoning.  It 
assumes  that  it  is  the  business  of  induction  to  count 
instances.  When  the  examination  and  enumeration  is 
exhaustive,  the  results  can,  of  course,  be  summed  up  in 
a  general  proposition  which  is  absolutely  certain.  But 

1  Jevons,  Elementary  Lessons  in  Logic,  pp.  212-213. 


1 88  ENUMERATION  AND   STATISTICS 

where  the  counting  is  incomplete,  where  all  the  possible 
cases  cannot  be  examined,  the  conclusion  is  regarded 
as  uncertain.  Now,  this  could  be  accepted  as  an  ac- 
count of  induction,  only  if  it  were  maintained  that  this 
process  aims  merely  at  a  summation  of  particular  in- 
stances. We  have  already  seen,  however,  that  the  real 
object  of  inductive  inference  is  to  discover  the  general 
law  or  principle  which  runs  through  and  connects  a 
number  of  particular  instances.  It  is,  of  course,  true 
that  we  shall  be  more  likely  to  obtain  a  correct  insight 
into  the  nature  of  the  law  from  an  examination  of  a 
large  number  of  cases  than  from  that  of  a  small  number. 
But  the  discovery  of  the  principle,  and  not  the  number 
of  instances,  is  the  main  point.  If  the  purpose  of  the 
induction,  the  discovery  of  the  universal  principle,  can 
be  adequately  attained,  one  case  is  as  good  as  a  hun- 
dred (cf.  §  88). 

The  truth  seems  rather  to  be  that  enumeration  is  merely  the 
beginning,  rather  than  the  end  of  the  inductive  process.  It  gives 
us  important  information  regarding  particular  instances  and  indi- 
viduals. But  in  itself  it  is  not  sufficient  to  bring  to  light  the  gen- 
eral law  that  explains  why  the  particular  objects  enumerated  are 
connected  together,  or  act  as  they  do.  Enumeration  plays  a  part 
as  a  method  of  observation,  but  it  affords  no  real  explanation  of 
the  particular  facts  with  which  it  deals.  Even  where  all  the  pos- 
sible cases  are  examined,  it  cannot  rightly  be  called  Perfect  In- 
duction, for  the  goal  of  Induction  is  explanation  by  means  of  a 
general  principle.  The  requirements  of  inductive  science  are  not 
completely  fulfilled,  for  example,  when  an  examination  of  Mercury, 
Venus,  Mars,  and  all  the  other  known  planets  yields  the  proposi- 
tion :  '  All  the  planets  revolve  around  the  sun  in  elliptical  orbits.' 
The  ( all '  in  this  proposition  denotes  simply  an  aggregate  of  indi- 
viduals. It  is  merely  an  expression  of  fact.  The  reasons  necessary 


§5i-     STATISTICS   AND   STATISTICAL   METHODS      189 

to  explain  the  fact  are  not  reached  by  enumeration  ;  in  order  to  ob- 
tain them  it  is  necessary  that  further  work  shall  be  done  by  think- 
ing, and  that  the  process  of  induction  shall  be  carried  further. 

The  conclusion  which  we  reach,  then,  is  that  no 
process  of  enumeration  has  any  claim  to  the  title  of 
Perfect  Induction.  Enumeration  is  the  beginning, 
rather  than  the  end  of  the  inductive  procedure. 
Nevertheless,  it  is  exceedingly  useful  as  a  preliminary 
step  and  preparation  for  scientific  explanation.  The 
number  of  stamens  and  pistils  which  a  plant  contains, 
or  the  number  of  tympanic  bones  possessed  by  an  ani- 
mal, is  often  of  the  greatest  service  in  classification. 
And  classification,  although  it  is  by  no  means  the  end 
of  scientific  investigation,  is  in  many  of  the  sciences  a 
most  essential  and  important  step  towards  it.  The  task 
of  explaining  the  infinite  variety  of  natural  objects 
would  be  a  hopeless  one,  if  it  were  not  possible  to 
discover  similarities  of  structure,  in  virtue  of  which 
things  can  be  grouped  together  in  classes.  To  this, 
enumeration  in  a  very  great  degree  contributes. 

§  51.  Statistics  and  Statistical  Methods.  —  Statistical 
methods  depend  upon  enumeration.  They  aim  at  mak- 
ing the  process  of  counting  as  exact  and  precise  as  pos- 
sible. Modern  science  has  come  to  understand  that  its 
first  task  must  be  to  become  acquainted,  as  completely 
as  possible,  with  the  nature  of  the  facts  presented  to  it 
by  experience.  And,  for  this  purpose,  the  careful  classi- 
fication and  precise  enumeration  of  particulars  afforded 
by  statistics,  is  often  of  the  greatest  importance.  "  The 
extent  to  which  the  statistical  method  prevails,  and 


I QO  ENUMERATION  AND   STATISTICS 

everything  is  counted,"  says  Professor  Sigwart,  "is 
another  instance  of  the  fundamental  difference  between 
ancient  and  modern  science."  l  It  would,  of  course,  be 
impossible  to  enter  here  into  a  full  description  of  the 
methods  employed  by  statistical  science.  The  method- 
ology of  every  science  must  be  learned  by  actual  prac- 
tice within  the  particular  field.  What  we  are  interested 
in  from  a  logical  point  of  view  is  the  purpose  which  sta- 
tistical investigation  seeks  to  fulfil,  and  the  part  which 
it  plays  in  rendering  our  knowledge  exact  and  syste- 
matic. 

We  notice,  in  the  first  place,  that  the  class  of  facts 
to  which  statistics  are  applied  has  two  main  character- 
istics :  the  subject  dealt  with  is  always  complex,  and 
capable  of  division  into  a  number  of  individual  parts  or 
units  ;  and,  secondly,  it  is  also  of  such  a  nature  that 
the  underlying  law  or  principle  of  the  phenomena  to  be 
investigated  cannot  be  directly  discovered.  Thus,  we 
employ  statistics  to  determine  the  death-rate  of  any 
country  or  community,  or  the  ratio  between  the  num- 
ber of  male  and  of  female  births.  It  is  clear  that  it  is 
impossible  to  make  use  of  experiment  when  we  are  deal- 
ing with  facts  of  this  kind,  because  the  conditions  are  not 
under  our  control.  If  it  were  possible,  for  example,  to 
determine  exhaustively  the  general  laws  according  to 
which  the  various  meteorological  changes  are  coordinated 
with  their  conditions,  we  should  not  trouble  ourselves  to 
count  and  register  the  separate  instances  of  changes  in 
the  weather.  Nor,  if  we  knew  exactly  the  general  condi- 

1  Logic  (Eng.  trans.),  Vol.  I.,  p.  286. 


§  5L     STATISTICS   AND   STATISTICAL   METHODS       IQI 

tions  under  which  any  given  human  organism  in  contact 
with  its  environment  would  cease  to  exist,  should  we 
count  the  individual  cases  of  death.  "  In  proportion  as 
we  are  unable  to  reduce  the  particular  event  to  rules  and 
laws,  the  numeration  of  particular  objects  becomes  the 
only  means  of  obtaining  comprehensive  propositions 
about  that  which  is,  for  our  knowledge,  fortuitous  ;  as 
soon  as  the  laws  are  found,  statistical  numeration  ceases 
to  be  of  interest.  There  was  some  interest  in  counting 
how  many  eclipses  of  the  moon  and  sun  took  place  year 
by  year,  so  long  as  they  occurred  unexpectedly  and  in- 
explicably ;  since  the  rule  has  been  found  according  to 
which  they  occur,  and  can  be  calculated  for  centuries 
past  and  to  come,  that  interest  has  vanished.  But  we 
still  count  how  many  thunder-storms  and  hail-storms 
occur  at  a  given  place,  or  within  a  given  district,  how 
many  persons  die,  and  how  many  bushels  of  fruit  a 
given  area  produces,  because  we  are  not  in  a  position  to 
calculate  these  events  from  their  conditions."  l 

In  cases  like  those  mentioned  above,  where  we  are 
as  yet  unable  to  determine  the  general  laws  which  are 
at  work,  we  call  to  our  aid  statistical  enumeration. 
There  are  two  main  advantages  to  be  derived  from  the 
employment  of  this  method.  In  the  first  place,  it  con- 
tributes directly  towards  a  clear  and  comprehensive 
grasp  of  the  facts.  Instead  of  the  vague  impression  de- 
rived from  ordinary  observation,  statistics  enable  us  to 
state  definitely  the  proportion  of  fine  and  rainy  days 
during  the  year.  Statistical  enumeration  is  thus  one 

1  Sigwart,  'Logic  (Eng.  trans.),  Vol.  II.,  p.  483. 


1 92  ENUMERATION  AND   STATISTICS 

of  the  most  important  means  of  rendering  observation  ex- 
act and  trustworthy,  and  of  summing  up  its  results  in  a 
convenient  and  readily  intelligible  form.  It  is  of  the 
utmost  importance  when  dealing  with  complex  groups  of 
phenomena,  to  have  a  clear  and  comprehensive  view  of 
the  facts  of  the  case.  Thus,  when  trying  to  understand 
the  nature  of  society,  it  is  necessary  to  determine  accu- 
rately by  means  of  statistics,  such  facts  as  the  number 
of  male  and  of  female  births,  the  death-rate,  the  pro- 
portion of  marriages,  the  age  of  marriage,  etc.  But, 
in  the  second  place,  statistics  often  serve  to  reveal 
quantitative  correspondences  OP  uniformities  between 
two  groups  of  phenomena,  and  thus  suggest  that  some 
causal  connection  exists  between  them.  It  is  found, 
for  example,  that  the  number  of  births  in  any  given 
country  varies  inversely  as  the  price  of  food  during  the 
previous  year.  Now  this  fact  at  once  suggests  the  ex- 
istence of  certain  physiological  and  psychological  laws 
which  may  serve  to  bring  these  facts  into  causal  rela- 
tion. In  many  cases,  such  correspondences  serve  only 
to  confirm  our  expectation  of  the  presence  of  a  causal 
law,  which  is  based  on  other  grounds.  Thus  we  should 
naturally  expect  that  there  would  be  a  relatively  greater 
number  of  cases  of  fever  in  a  town  which  had  an  insuf- 
ficient water  supply,  or  an  antiquated  system  of  sewer- 
age, than  in  a  town  where  these  matters  were  properly 
provided  for ;  and  statistics  might  bear  out  our  conclu- 
sions. In  general,  however,  it  may  be  said  that  causal 
laws  are  suggested,  not  by  corresponding  uniformities, 
but  by  corresponding  variations,  as  shown  by  the  sta- 
tistics of  different  sets  of  facts.  So  long  as  the  death- 


§  5i.    STATISTICS  AND   STATISTICAL  METHODS      193 

rate,  for  example,  shows  a  constant  ratio  to  the  pop- 
ulation, no  causal  inference  is  suggested  ;  but  if  the 
annual  number  of  deaths  increases  or  decreases  consid- 
erably, we  are  led  to  look  for  some  variation  from  the 
normal  in  some  coincident  group  of  phenomena.  And 
if  it  is  found  that  the  variation  in  the  death-rate  has 
been  accompanied  by  unusually  favourable  or  unfavoura- 
ble conditions  of  weather,  the  presence  or  absence  of 
epidemics,  or  any  similar  circumstances,  there  will  be  at 
least  a  presumption  that  a  causal  relation  exists  between 
these  two  sets  of  events.  From  a  certain  likeness 
or  quantitative  resemblance  between  the  variations  of 
two  distinct  classes  of  phenomena,  we  are  led  to  the 
hypothesis  of  their  causal  connection. 

Statistical  enumeration  is  frequently  employed  to  determine  the 
average  of  a  large  number  of  instances  of  a  particular  kind.  This  is 
obtained  by  dividing  the  sum  of  the  given  numbers  by  the  number 
of  individuals  of  which  account  is  taken.  In  this  way  a  general 
average  is  reached  which  does  not  necessarily  correspond  exactly 
with  the  character  of  any  individual  of  the  group.  It  represents  a 
purely  imaginary  conception,  which  omits  individual  differences  and 
presents  in  an  abbreviated  form  the  general  character  of  a  whole 
class  or  group.  In  this  way,  by  the  determination  of  the  average,  it 
becomes  easier  to  compare  complex  groups  with  one  another.  Thus, 
when  the  average  height  of  Frenchmen  and  Englishmen  has  been 
determined,  comparison  is  at  once  made  possible.  For  the  mean 
or  average  of  a  number  of  individuals,  or  set  of  instances,  however, 
we  can  infer  nothing  regarding  the  character  of  any  particular  indi- 
vidual, or  of  any  particular  instance.  What  is  determined  by  the 
method  of  averages  is  the  general  nature  of  the  group,  as  represented 
by  the  average  or  typical  individual.  But  this  method  does  not  en- 
able us  to  infer  anything  regarding  the  character  of  any  member  of 
the  group,  A,  or  B.  When  exact  statistics  are  obtainable,  however, 
o 


IQ4  ENUMERATION  AND   STATISTICS 

it  is  possible  to  show  what  the  probabilities  are  in  reference  to  any 
particular  case,  so  long  as  the  peculiar  circumstances  which  belong 
to  each  instance  are  not  considered,  and  each  case  is  reckoned  simply 
as  one  unit  of  the  group.  This  is,  of  course,  the  principle  employed 
by  the  method  of  mathematical  probabilities.  It  will  be  sufficient 
here  to  indicate  the  general  method  of  procedure  in  such  cases. 

§  52.  The  Calculation  of  Chances.  —  There  is,  of  course, 
no  such  thing  as  '  chance,'  regarded  as  a  power  which 
controls  and  governs  events.  When  we  speak  of  some- 
thing happening  'by  chance,'  or  of  some  occurrence  as 
'  probable,'  we  are  expressing  merely  a  deficiency  in  our 
own  knowledge.  "There  is  no  doubt  in  lightning  as 
to  the  point  it  shall  strike ;  in  the  greatest  storm  there 
is  nothing  capricious ;  not  a  grain  of  sand  lies  upon  the 
beach  but  infinite  knowledge  would  account  for  its  lying 
there  ;  and  the  course  of  every  falling  leaf  is  guided  by 
the  same  principles  of  mechanics  as  rule  the  motions  of 
the  heavenly  bodies."1  To  assert  that  anything  hap- 
pens by  chance,  then,  is  simply  to  confess  our  ignorance 
of  the  causes  which  are  operative. 

It  is  clear  that  we  are  in  this  position  regarding  many 
of  the  ordinary  events  which  belong  to  the  future.  Be- 
cause of  my  ignorance  of  the  causes  at  work,  I  can  only 
say,  '  It  may  rain  to-morrow.'  It  is  impossible  to  tell 
upon  which  side  a  penny  will  fall  at  any  particular 
throw,  or  what  card  may  be  drawn  from  a  pack.  But  in 
cases  like  these,  we  have  to  accept,  for  lack  of  anything 
better,  a  numerical  statement  of  the  chances  for  any 
particular  event.  Thus  we  know  that,  since  there 

1  Jevons,   The  Principles  of  Science,  Vol.  I.,  p.  2^. 


§  52.    THE  CALCULATION   OF  CHANCES  195 

are  only  two  sides  upon  which  a  penny  can  fall,  the 
chances  of  throwing  heads  in  any  trial  is  J.  Similarly, 
there  are  four  chances  out  of  fifty-two  of  drawing  an 
ace  from  a  pack  of  cards.  The  chance  of  obtaining 
an  ace  by  any  draw  is  therefore  -£$=^$-  These  figures 
express  the  mathematical  chances.  Experience  of  a 
limited  number  of  instances  may,  however,  sometimes 
appear  to  show  a  lack  of  harmony  between  the  mathe- 
matical and  the  actual  chances.  But  in  proportion  as 
the  number  of  trials  is  increased,  the  result  is  found  to 
approximate  more  and  more  nearly  to  the  mathematical 
expectation.  In  twenty  throws  of  a  penny  or  a  die,  we 
should  not  be  surprised  to  find  that  the  result  differed 
from  the  fraction  expressing  the  mathematical  chances. 
But  this  discrepancy  would  tend  to  disappear  as  the 
number  of  cases  was  increased.  Jevons  illustrated  this 
by  actual  trial,  using  a  number  of  coins  at  a  time.  Out 
of  a  total  of  20,480  throws,  he  obtained  a  result  of  10,353 
heads.  On  the  result  of  the  experiment  he  remarks : 
"  The  coincidence  with  theory  is  pretty  close,  but  con- 
sidering the  large  number  of  throws  there  is  some 
reason  to  suspect  a  tendency  in  favor  of  heads."1 

Apart  from  the  simple  and  somewhat  artificial  cases 
where  we  are  concerned  with  coins  and  dice,  etc.,  it  is 
impossible  to  determine  with  mathematical  precision  the 
chances  for  or  against  any  event.  In  cases  where  the 
whole  series  of  possibilities  does  not  lie  before  us,  we 
have  to  base  our  calculations  for  the  future  on  what 
is  known  regarding  the  frequency  with  which  the  events 

1  Jevons,  loc.  cit.  Vol.  I.,  p.  230. 


196  ENUMERATION  AND   STATISTICS 

under  consideration  have  occurred  in  the  past.  Now 
the  results  of  the  last  paragraph  make  it  clear  that  it  is 
of  the  utmost  importance  that  the  statistics,  which  are 
taken  as  the  basis,  shall  be  as  full  and  comprehensive 
as  possible.  It  is  evident,  for  example,  that  serious 
errors  would  be  likely  to  arise,  if  the  death-rate  for  a 
single  year,  or  for  a  single  county  or  town,  were  taken 
as  typical  of  the  country  as  a  whole.  To  render  sta- 
tistics trustworthy,  they  must  be  extended  over  a  consid- 
erable period  of  time,  and  over  a  large  extent  of  country, 
so  as  to  eliminate  the  accidents  due  to  a  particular  time 
or  to  a  particular  locality. 

When  this  has  been  done,  however,  and  statistics  have  been  ob- 
tained that  have  a  right  to  be  regarded  as  really  typical,  the  chances 
in  any  individual  instance  can  be  readily  shown.  Thus  we  find  that 
out  of  one  thousand  children  born,  about  two  hundred  and  fifty  die 
before  the  age  of  six  years.  The  chances,  then,  at  birth,  that  any 
child  will  reach  this  age,  are  TT0^j-  or  f .  Again,  it  is  found  that 
only  about  two  persons  in  one  thousand  live  to  be  ninety  years  old. 
So  that  the  probability  of  any  child  living  to  this  age  would  be  ex- 
pressed by  the  fraction  y^  or  ^.  This  is  essentially  the  princi- 
ple upon  which  life  insurance  companies  proceed.  Their  business  is 
conducted  on  the  assumption  that  there  will  be  an  approximately 
constant  death-rate,  though  they  cannot  foretell  what  particular  indi- 
viduals are  to  die  in  any  year.  It  thus  becomes  possible  to  calculate 
what  losses  from  death  may  be  expected  each  year.  Suppose  that 
it  is  found  that  the  annual  death-rate  among  men  of  a  certain  age 
throughout  the  country  is  twenty  out  of  every  thousand.  If  each 
man's  life  were  insured  for  $1000,  the  loss  to  the  company  from 
this  source  would  be  $20,000.  To  compensate  for  this  loss,  the 
company  would  be  obliged  to  demand  an  annual  payment  of  $20 
from  each  of  the  one  thousand  individuals  in  the  class.  Of  course, 
the  actual  computations  upon  which  insurance  is  based  in  concrete 


§  52.    THE  CALCULATION  OF  CHANCES  197 

cases  are  vastly  more  complex  than  this,  and  many  other  consider- 
ations arise  of  which  account  has  to  be  taken.  But  the  general 
principle  involved  is,  that  by  taking  a  sufficiently  large  number  of 
cases,  chance  can  be  almost  eliminated.  We  can  have  no  means 
of  determining  whether  any  healthy  individual  will  or  will  not  die 
before  the  end  of  the  year.  There  would  be  a  very  serious  risk, 
amounting  practically  to  gambling,  in  insuring  his  life  alone.  But 
the  transaction,  as  we  have  seen,  is  no  longer  a  mere  speculation 
when  a  large  number  of  individuals  are  concerned ;  for  the  actual 
loss  can  be  accurately  foretold  and  provided  for. 

References 

C.  Sigwart,  Logic,  §§  101,  102. 

J.  G.  Hibben,  Inductive  Logic,  Ch.  XV. 

L.  T.  Hobhouse,  The  Theory  of  Knowledge,  Pt.  II.  Ch,  XI. 

J.  S.  Mill,  Logic,  Bk.  III.  Ch.  XVIII. 

B.  Bosanquet,  Logic,  Vol.  I.,  pp.  I28ff. 


CHAPTER  XV 

METHODS   OF   OBSERVATION 

Determination  of  Causal  Relation 

§  53.  Mill's  Experimental  Methods.  —  So  far,  we  have 
been  dealing  with  the  methods  employed  in  discovering 
the  nature  of  particular  things.  We  have  been  con- 
sidering how  our  knowledge  of  the  qualities  and  quanti- 
ties of  objects  may  be  made  as  exact  and  complete  as 
possible,  but  almost  nothing  has  yet  been  said  regard- 
ing the  connection  of  things.  Our  experience,  however, 
is  not  made  up  of  isolated  facts  and  events.  We  can 
scarcely  be  said  to  know  at  all,  until  we  become  aware 
that  certain  parts  of  our  experience  are  united,  like  the 
links  of  a  chain,  one  part  involving  another.  And,  as 
has  been  already  frequently  pointed  out,  the  growth  of 
knowledge  is  constantly  bringing  to  light  new  connec- 
tions between  facts  that  were  previously  taken  to  be 
independent  of  each  other.  Of  these  principles  of 
connection,  the  most  universal  and  important  is  that 
of  cause  and  effect.  Thus  we  say  that  everything 
which  happens  has  its  cause,  and  is  in  turn  followed 
by  its  effect.  What  rule,  or  rules,  can  now  be  given 
which  will  enable  one  to  discover  what  is  the  cause  or 
the  effect  of  an  event  in  any  particular  case  ? 

Before  we  proceed  to  the  answer  of  this  question,  however,  it  is 
necessary  to  explain  briefly  what  is  meant  in  science  by  the  relation 

198 


§  53-     MILL'S   EXPERIMENTAL   METHODS  199 

of  cause  and  effect.  As  the  terms  are  used  in  modern  scientific 
investigation,  a  cause  of  any  phenomenon  is  that  which  necessarily 
and  invariably  precedes  it;  and  an  effect  is  what  follows,  in  the 
same  uniform  way,  some  event  which  has  gone  before  (cf.  §  84). 
To  determine  the  causal  relation  between  phenomena,  then,  is  to 
discover  what  events  or  circumstances  always  accompany  each 
other  as  antecedent  and  consequent.  Now,  as  will  appear  when 
we  come  to  describe  the  methods  actually  employed,  it  is  very  often 
impossible  to  do  this  by  means  of  direct  observation.  Reasoning 
and  experiment  have  oftentimes  to  be  summoned  to  the  aid  of 
observation  in  distinguishing  between  events  which  are  merely 
accidentally  conjoined,  and  those  which  are  necessarily  connected 
as  cause  and  effects.  But,  as  has  been  already  shown  (§§  48,  49), 
there  is  no  hard  and  fast  distinction  to  be  made  between  methods 
of  observation  and  methods  of  explanation.  To  discover  the  in- 
variable antecedent  of  a  phenomenon  is  at  least  the  beginning  of 
explanation.  Thus  B  is  explained  to  some  extent  when  I  am  able 
to  point  to  A  as  its  invariable  antecedent.  Nevertheless,  since  this 
connection  of  A  and  B  is  itself  a  fact  which  may  be  observed,  its 
discovery  may,  I  think,  be  fairly  said  to  belong  to  observation  rather 
than  to  explanation.  Explanation,  in  its  complete  form,  carries  one 
beyond  the  mere  fact  of  connection  to  its  reasons.  At  the  stage 
we  have  now  reached,  however,  the  problem  is  to  show  what  other 
phenomenon,  or  group  of  phenomena,  is  necessarily  and  uniformly 
connected  with  a  given  event  or  circumstance. 

The  methods  by  which  such  a  law  of  connection  may 
be  established  were  first  formulated  by  Mill  in  his  Logic. 
He  stated,  in  general  terms,  the  principles  which  were 
already  in  use  in  scientific  procedure.  Mill  gives  five 
separate  canons,  but,  as  he  himself  recognizes,  there 
are  but  two  main  principles  involved.  "The  simplest 
and  most  obvious  modes  of  singling  out  from  among 
the  circumstances  which  precede  or  follow  a  phenome- 
non, those  with  which  it  is  really  connected  by  an 


200  CAUSAL  DETERMINATION 

invariable  law  are  two  in  number :  One  is  by  com- 
paring together  different  instances  in  which  the  phe- 
nomenon occurs.  The  other  is  by  comparing  together 
instances  in  which  the  phenomenon  does  occur  with 
instances  in  other  respects  similar  in  which  it  does  not. 
These  two  methods  may  be  respectively  denominated 
the  Method  of  Agreement,  and  the  Method  of  Differ- 
ence." *  Of  the  other  three  methods  mentioned  by 
Mill,  one  —  the  Joint  Method  of  Agreement  and  Dif- 
ference —  is,  as  the  name  implies,  a  direct  combination 
of  the  first  two,  while  the  Method  of  Residues  and  the 
Method  of  Concomitant  Variations  are  corollaries  from 
the  same  principles.  We  shall  now  proceed  to  state 
and  illustrate  these  canons. 

§  54.  The  Method  of  Agreement.  —  The  principle  upon 
which  this  method  proceeds  is  stated  in  the  following 
way  by  Mill :  "If  two  or  more  instances  of  the  phenome- 
non under  investigation  have  only  one  circumstance  in 
common,  the  circumstances  in  which  alone  all  the  in- 
stances agree  is  the  cause  (or  effect)  of  the  given  phenome- 
non." The  purpose  of  this  rule,  it  will  be  remembered, 
is  to  help  us  to  determine  what  particular  facts  in  our 
experience  are  connected  as  causes  and  effects.  If  the 
problem  is  to  find  the  cause  of  some  phenomenon,  the 
canon  may  be  illustrated  in  the  following  way.  Let 
P1,  P2,  P3  represent  different  instances  of  a  phenome- 
non, P,  whose  cause  is  to  be  ascertained,  And  suppose 
that  we  are  able  to  analyze, 

1  Mill,  Logic,  Bk.  III.  Ch.  VIII.  §  1 


§  54-    THE  METHOD   OF  AGREEMENT  2OI 

the  antecedents  of  P1  into  abed ; 
the  antecedents  of  P2  into  gfcm  ; 
the  antecedents  of  P3  into  klnc. 

Now  it  is  clear  that  c  is  the  sole  circumstance  in  which 
the  antecedents  of  all  these  instances  of  P  agree.  We 
should  be  justified  in  concluding,  therefore,  according  to 
this  method,  that  c  is  probably  the  cause  of  the  phe- 
nomenon under  investigation,  P.  We  may,  then,  adopt 
Jevons's  formula  for  discovering  the  cause  of  any  given 
phenomenon  by  this  method  :  "The  sole  invariable  ante- 
cedent of  a  phenomenon  is  probably  its  cause" 

If,  now,  we  wished  to  discover  the  effect  of  some- 
thing which  happens,  it  would  be  necessary  to  deter- 
mine, by  observing  a  number  of  instances,  what  common 
circumstance  can  be  found  among  the  events  which 
follow  it. 

If  Q1  were  followed  by  fghk, 

and  Q2  were  followed  by  Imgc, 

and  Q3  were  followed  by  grst, 

we  should  be  able  to  say  that  Q  and  g  were  connected 
as  cause  and  effect.  The  rule  might  then  be  expressed  : 
The  sole  invariable  consequent  of  a  phenomenon  is  prob- 
ably its  effect. 

When  antecedents  and  consequents  are  thus  repre- 
sented schematically  by  means  of  letters,  it  is  easy  to 
perceive  at  once  the  common  circumstance  in  a  number 
of  instances.  But  the  facts  and  events  of  the  real  world 
are  not  separated  off  from  each  other  in  this  way.  The 
common  circumstance  in  which  a  number  of  instances 
agree  has  to  be  separated  out  by  analysis  from  the  varia- 


202  CAUSAL  DETERMINATION 

ble  elements  which  form  part  of  the  different  antecedents 
and  consequents.  In  order  to  discover  the  common 
characteristic,  it  is  necessary  that  we  should  be  able 
to  analyze  a  complex  phenomenon  into  its  constituent 
parts,  and  should  also  be  able  to  recognize  the  common 
element  as  common,  though  it  may  appear  in  wholly 
different  circumstances.  This  will  become  evident  by 
considering  a  number  of  concrete  cases  in  which  this 
method  may  be  employed. 

If  a  number  of  cases  of  typhoid  fever  were  to  appear 
at  about  the  same  time  in  a  community,  one  would  nat- 
urally wish  to  explain  this  phenomenon  by  tracing  it  to 
its  cause;  and  to  do  this  one  would  try  to  discover 
some  circumstance  which  was  the  common  antecedent 
of  all  the  cases.  The  water  supply  might  first  be  ex- 
amined. But  if  it  were  found  that  this  were  derived 
from  entirely  different  sources  in  the  different  cases,  we 
should  probably  conclude  that  the  explanation  must  be 
sought  elsewhere.  Suppose  that  as  a  result  of  careful 
analysis  it  was  discovered  that  all  the  individuals  pros- 
trated with  the  fever  had  eaten  oysters  bought  at  the 
same  market.  If  this  were  the  only  common  circum- 
stance discoverable  after  careful  investigation,  we  should 
conclude  that  probably  the  oysters  were  the  cause  of 
the  fever.  The  process  of  analysis  could  be  pushed 
still  further,  if  one  wished,  in  order  to  determine  more 
exactly  the  precise  source  of  the  infection ;  e.g.,  it  might 
be  found,  as  a  result  of  further  inquiry,  that  the  water 
in  which  the  oysters  were  kept  was  vitiated  by  a  sewer. 

Another  example  of  the  method  of  agreement  which 
is  often  quoted  by  logicians  may  be  given.  One  would 


§  54-    THE  METHOD  OF  AGREEMENT  2O3 

naturally  suppose  that  the  colours  and  lines  of  mother-of- 
pearl  were  due  to  the  chemical  or  physical  character  of 
the  substance  itself.  Sir  David  Brewster,  however, 
happened  to  take  an  impression  of  a  piece  of  mother- 
of-pearl  in  beeswax  and  resin,  and  was  surprised  to  see 
the  colours  reproduced  upon  its  surface.  He  then  took 
a  number  of  other  impressions  in  balsam,  gum-arabic, 
lead,  etc.,  and  found  the  iridescent  colours  repeated  in 
every  case.  In  this  way  he  proved  that  the  colours  were 
caused  by  the  form  of  the  substance,  and  not  by  its 
chemical  qualities  or  physical  composition.  The  dif- 
ferent substances,  wax,  balsam,  lead,  etc.,  in  which  the 
phenomenon  of  colour  appeared,  had  nothing  in  common 
except  the  form.  This,  therefore,  according  to  the 
method  of  agreement,  was  properly  regarded  as  the 
cause  of  the  phenomenon  to  be  explained. 

An  example  of  the  application  of  this  method  to  the 
discovery  of  the  effect  of  a  phenomenon  may  now  be 
given.  Let  us  suppose  that  the  problem  is  to  determine 
the  effect  of  some  proposed  legislation.  It  is  necessary, 
of  course,  to  refer  to  other  instances  where  this  legisla- 
tion has  been  put  in  force.  Let  us  suppose  that  in  one 
case  what  followed  the  enactment  of  the  law  under  con- 
sideration was  falling  off  of  revenue,  increase  of  immi- 
gration, good  crops,  etc.,  and  in  a  second,  revival  of 
ship-building,  rainy  weather,  and  increase  of  immigra- 
tion ;  and  that  in  other  instances  where  still  other 
conditions  prevailed,  the  number  of  immigrants  still 
continued  to  increase.  Since  this  latter  circumstance  is 
the  only  one  which  follows  invariably  upon  the  enact- 
ment of  the  law,  we  are  justified  in  concluding,  after  a 


204  CAUSAL  DETERMINATION 

certain  number  of  observations,  that  it  is  necessarily 
connected  with  the  law  as  its  result.  It  is  important 
to  note  that  the  conclusions  reached  by  this  method 
are  greatly  strengthened  by  increasing  the  number  of 
observations,  and  by  taking  instances  as  dissimilar  in 
character  as  possible. 

The  method  of  Agreement  by  itself,  however,  is  not  able  to 
afford  us  certainty  in  every  case.  We  have  spoken  of  the  cause  as 
'the  invariable  antecedent,'  and  of  the  effect  as  'the  invariable  con- 
sequent.1 So  long,  then,  as  we  are  dealing  with  events  which  fol- 
low each  other,  there  is  no  difficulty  in  perceiving  which  is  cause, 
and  which  effect.  But  we  are  often  called  upon  to  investigate  the 
relation  between  phenomena  that  are  more  permanent  in  character. 
And  it  is  then  not  at  all  easy  to  determine  by  means  of  the  method 
of  Agreement  which  is  cause  and  which  is  effect.  Poverty  and  in- 
temperance, for  example,  are  found  conjoined  so  frequently  as  to 
make  it  evident,  apart  from  other  considerations,  that  some  causal 
relation  exists  between  them.  It  might  be  maintained  with  appar- 
ently equal  show  of  reason,  that  the  former  is  the  cause,  or  the  effect, 
of  the  latter.  Again,  is  one  to  say  that  ignorance  is  the  cause  or  the 
effect  of  moral  degradation  ?  There  seems  to  be  no  method  of  de- 
termining which  is  antecedent  and  which  consequent.  As  a  matter 
of  fact,  it  is  probably  true  in  such  cases  that  the  phenomena  act 
and  react  upon  each  other :  that  each  term,  in  other  words,  is  at 
once  both  cause  and  effect. 

There  is  still  another  circumstance  which  renders  uncertain  the 
results  of  the  method  of  Agreement.  We  have  proceeded  on  the 
assumption  that  the  given  phenomenon  is  always  produced  by 
the  same  cause ;  and,  on  the  other  hand,  that  the  effects  of  different 
causes  are  always  different.  But  this  is  not  so ;  heat,  for  example, 
may  be  caused  by  combustion,  or  by  friction,,  or  electricity.  The 
fact  that  an  effect  may  be  produced  by  any  one  of  several  causes,  is 
what  is  meant  by  the  phrase  'Plurality  of  Causes.1  Again,  neither 
the  cause  nor  the  effect  need  be  composed  of  a  simple  phenomenon, 


§  55-    THE   METHOD   OF  DIFFERENCE  2O5 

or  single  circumstance,  as  has  been  supposed.  Indeed,  so  far  as 
observation  can  show,  antecedents  and  consequents  usually  seem  to 
consist  of  complex  sets  of  circumstances.  The  difficulty  with  the 
method  of  Agreement  is  that  it  does  not  push  the  process  of  analysis 
far  enough  to  enable  us  to  establish  completely  a  law  of  causal  rela- 
tion. The  fact  of  Agreement  between  phenomena  often  serves,  how- 
ever, to  suggest  a  law  of  connection.  This  law  has  afterwards  to  be 
tested  by  the  other  methods,  especially  by  the  method  of  Difference. 

§  55.  The  Method  of  Difference.  —  According  to  the 
method  of  Agreement,  we  compare  a  number  of  diverse 
instances,  in  all  of  which  a  given  phenomenon  occurs, 
and  endeavour  to  discover  some  circumstance  which  is 
invariably  present.  The  method  of  Difference,  on  the 
other  hand,  compares  an  instance  in  which  a  phenome- 
non occurs  with  another  as  nearly  similar  to  it  as  possi- 
ble, in  which  it  does  not  occur.  Its  canon  is  expressed 
by  Mill  as  follows:  " If  an  instance  in  which  the  phe- 
nomenon under  investigation  occurs,  and  an  instance  in 
which  it  does  not  occur,  have  every  circumstance  in 
common  save  one,  that  one  occurring  only  in  the  former ; 
the  circumstance  in  which  alone  the  two  instances  differ 
is  the  effect  or  the  cause  or  an  indispensable  part  of 
the  cause,  of  the  phenomenon'''  It  will  perhaps  make 
the  matter  clearer  to  say :  '  whatever  alone  is  present 
in  a  case  when  the  phenomenon  to  be  investigated 
occurs,  and  absent  in  another  when  that  phenomenon 
does  not  occur,  other  circumstances  remaining  the 
same,  is  causally  connected  with  that  phenomenon.' 
That  is,  by  means  of  this  method  we  compare  two 
instances  which  differ  only  in  the  fact  that  the  phe- 
nomenon in  which  we  are  interested,  is  present  in  the 


2O6  CAUSAL  DETERMINATION 

one,  and  absent  in  the  other.     If  now  the  two  cases  are 
represented  in  this  way, 

PHK  conjoined  with  alg, 
and    HK  conjoined  with   Ig, 

we  conclude  at  once  that  P  is  causally  connected  with  a. 

Almost  any  instance  in  which  experiment  is  em- 
ployed will  serve  to  illustrate  this  method.  If  a  bell  is 
rung  in  a  jar  containing  air,  the  sound  will  of  course  be 
heard  at  any  ordinary  distance.  But  after  having  re- 
moved the  air  by  means  of  an  air-pump,  let  the  bell  be 
again  struck.  It  will  now  be  found  that  the  sound  is  no 
longer  heard.  When  the  two  cases  are  compared,  it  is 
at  once  evident  that  the  only  difference  in  the  antece- 
dents is  the  presence  of  the  air  in  the  one  case,  and  its 
absence  in  the  other.  When  the  air  was  present,  the 
sound  was  heard  ;  when  it  was  absent,  the  sound  was 
not  heard.  We  conclude,  therefore,  that  the  perception 
of  sound  is  causally  connected  with  the  presence  of 
atmospheric  air.  Again,  we  can  prove  that  the  so-called 
1  taste  '  of  different  objects  depends  upon  smell,  by  tast- 
ing, say,  an  orange,  and  after  a  little  time  has  elapsed, 
tasting  it  a  second  time  while  holding  the  nose.  It 
will  be  found  in  this  latter  case  that  instead  of  the 
familiar  'orange  taste,'  one  senses  merely  'acid/  or 
'sweet.'  The  only  difference  in  the  two  trials  being 
that  in  the  former  the  organ  of  smell,  which  was  ex- 
cluded in  the  latter,  was  operative,  the  so-called  'orange 
taste '  is  proved  to  be  due  to  smell  rather  than  to  taste 
proper. 

An  essential  requirement  of  the  method  of  Difference 


§  55-    THE   METHOD   OF  DIFFERENCE  2O? 

is  that  only  one  circumstance  shall  be  varied  at  a  time. 
The  object  of  the  method  is  to  isolate  the  various  con- 
ditions which  go  to  make  up  a  complex  phenomenon, 
in  order  that  we  may  mark  the  effect  of  the  presence 
or  absence  of  each  one  individually.  Now,  in  observing 
what  goes  on  in  nature,  we  rarely  find  changes  in 
which  but  a  single  element  has  varied.  If  we  find  that 
to-day  is  cooler  than  yesterday,  we  may  be  inclined  to 
refer  the  change  to  the  thunder-storm  of  last  night. 
But  rain  also  accompanied  the  thunder-storm,  and  the 
direction  of  the  wind  has  changed.  So  that  it  is  im- 
possible in  such  cases  to  apply  the  method  of  difference. 
To  employ  this  method  successfully,  observation  usually 
must  be  supplemented  by  experiment.  In  performing 
experiments,  we  determine  what  conditions  are  to  be 
operative,  and  arrange  the  apparatus  so  as  to  carry  out 
our  purpose.  Having  thus  control  of  the  conditions,  we 
are  able  to  vary  them  at  pleasure.  In  this  way,  experi- 
ment becomes  an  instrument  by  means  of  which  analysis 
can  be  carried  further  than  is  possible  for  unaided  ob- 
servation. It  enables  us  to  separate  things  which  are 
usually  conjoined,  and  to  observe  the  result  of  each  when 
taken  by  itself.  In  employing  experiment,  however,  the 
greatest  care  must  always  be  taken  to  introduce  only 
one  new  condition  at  a  time,  or  at  least  only  one  new 
circumstance  which  can  in  any  way  influence  the  result. 
It  often  happens,  too,  as  Jevons  points  out,  that  the 
experimenter  is  not  aware  of  all  the  conditions  which 
are  operative  when  his  investigations  are  made.  "  Some 
substance  may  be  present,  or  some  power  may  be  in 
action  which  escapes  the  most  vigilant  examination. 


208  CAUSAL  DETERMINATION 

Not  being  aware  of  its  existence,  we  are  of  course 
unable  to  take  proper  measures  to  exclude  it,  and  thus 
determine  the  share  which  it  may  have  in  the  results  of 
our  experiments."  l  For  this  reason,  it  is  always  neces- 
sary that  experiments  should  be  repeated  by  different 
persons,  and  so  far  as  possible  under  varying  conditions. 
I  quote  two  examples  from  the  work  of  Jevons  to  which 
reference  has  just  been  made. 

"  One  of  the  most  extraordinary  instances  of  an  erroneous  opinion 
due  to  overlooking  interfering  agents  is  that  concerning  the  increase 
of  rainfall  near  the  earth's  surface.  More  than  a  century  ago  it  was 
observed  that  rain  gauges  placed  upon  church  steeples,  house-tops, 
and  other  elevated  places,  gave  considerably  less  rain  than  if  they 
were  on  the  ground,  and  it  has  very  recently  been  shown  that  the 
variation  is  most  rapid  in  the  close  neighborhood  of  the  ground. 
All  kinds  of  theories  have  been  started  to  explain  this  phenomenon  ; 
but  I  have  attempted  to  show  that  it  is  simply  due  to  the  interfer- 
ence of  wind  which  deflects  more  or  less  rain  from  all  the  gauges 
which  are  at  all  exposed  to  it. 

u  The  great  magnetic  power  of  iron  renders  it  a  constant  source  of 
disturbance  in  all  magnetic  experiments.  In  building  a  magnetic 
observatory  great  care  must  be  taken  that  no  iron  is  employed  in 
the  construction,  and  that  no  masses  of  iron  are  near  at  hand.  In 
some  cases,  magnetic  observations  have  been  seriously  disturbed  by 
the  existence  of  masses  of  iron  in  the  neighborhood.  In  Faraday's 
experiments  upon  feebly  magnetic  or  diamagnetic  substances,  he 
took  the  greatest  precautions  against  the  presence  of  any  disturbing 
substance  in  the  copper  wire,  wax,  paper,  and  other  articles  used  in 
suspending  the  test  objects.  It  was  his  invariable  custom  to  try  the 
effect  of  the  magnet  uppn  the  apparatus  in  the  absence  of  the  object 
of  experiment,  and  without  this  preliminary  trial  no  confidence 
could  be  placed  in  the  results."  2 

1  Jevotts,  Principles  of  Science,  Vol.  II.  p.  37. 

2  Jevons,  op.  cit.  pp.  40,  41. 


CHAPTER   XVI 

METHODS    OF    OBSERVATION 

Determination  of  Causal  Relation  (continued*) 

§  56.  The  Joint  Method  of  Agreement  and  Difference.  — • 
When  it  is  not  possible  to  obtain  experimental  proof 
directly,  recourse  is  often  had  to  what  Mill  has  called 
the  joint  method  of  Agreement  and  Difference.  This 
writer  has  given  the  following  expression  of  the  canon  : 
"  If  two  or  more  instances  in  which  the  phenomenon 
occurs  have  only  one  circumstance  in  common,  while 
two  or  more  instances  in  which  it  does  not  occur  have 
nothing  in  common  save  the  absence  of  that  circum- 
stance, the  circumstance  in  which  alone  the  two  sets 
of  instances  differ  is  the  effect,  or  the  cause,  or  an 
indispensable  part  of  the  cause,  of  the  phenomenon." 
This  method,  as  the  name  implies,  is  a  combination 
of  the  two  already  described.  We  may  perhaps  sim- 
plify Mill's  canon  somewhat  by  putting  the  matter  in 
the  following  way :  A  number  of  diverse  instances  hav- 
ing1 been  examined,  if  it  is  found  that  there  is  a  single 
circumstance  invariably  present  when  the  phenomenon 
under  investigation  is  present,  and  invariably  absent 
when  the  latter  is  absent,  this  circumstance  is  causally 
connected  with  that  phenomenon.  By  the  help  of  this 
method,  the  weakness  which  has  already  been  noticed 
in  the  method  of  Agreement  is  overcome.  We  first 
p  209 


210  CAUSAL  DETERMINATION 

compare  different  instances  in  which  the  phenomenon 
occurs.  If  these  are  found  to  agree  in  only  a  single 
circumstance,  we  conclude,  according  to  the  canon 
of  Agreement,  that  this  circumstance  is  probably  con- 
nected causally  with  the  phenomenon  in  which  we  are 
interested.  But  the  proof  is  not  yet  complete.  To 
really  prove  the  connection,  we  must  show  that  where- 
ever  this  circumstance  is  absent,  there  the  phenome- 
non is  also  absent. 

As  an  illustration  of  this  method,  we  may  take  the 
case  where  one  is  trying  to  decide  whether  some  stimu- 
lant like  coffee  or  tobacco  is  injurious  to  him  or  not.  If  a 
person  invariably  found  himself  troubled  with  insomnia 
or  nervousness  after  smoking,  and  if  this  seemed  to  him 
the  only  circumstance  in  his  mode  of  life  common  to  all 
these  occasions,  he  might  suspect  that  this  was  the  cause. 
That  is,  the  coincidence  or  agreement  between  the  habit 
and  ill-health  would  suggest  a  causal  relation.  But  as  yet, 
the  relation  would  be  only  suggested,  not  proved.  The 
method  of  Agreement,  as  we  have  already  seen,  only 
gives  us  probable  conclusions.  Here,  however,  we  have 
the  conditions  under  our  control,  and  can  resort  to  ex- 
periment and  the  method  of  Difference,  in  order  to  verify 
or  disprove  the  suggestion.  If  after  having  given  up 
smoking  for  a  reasonable  length  of  time,  a  man  found 
that  the  disagreeable  symptoms  still  continued,  he  would 
conclude  that  his  suspicion  was  unfounded.  But  if  it 
were  found  that  his  insomnia  and  nervousness  had  dis- 
appeared during  his  period  of  abstinence,  and  if  the 
sole  circumstance  common  to  all  these  days  and  nights 
of  exemption  was  the  absence  of  smoking,  he  would  be 


§57-    THE  METHOD  OF  CONCOMITANT  VARIATIONS      211 

forced  to  admit,  however  reluctant  he  might  be'  to  do  so, 
that  the  troublesome  physiological  derangements  were 
probably  connected  with  the  smoking  habit. 

§  57.  The  Method  of  Concomitant  Variations. — The 
methods  of  Agreement  and  Difference  are  employed, 
as  we  have  seen,  to  determine  what  events  are  necessa- 
rily connected  as  causes  and  effects.  By  examining  a 
considerable  number  of  instances,  and  by  comparing 
the  cases  in  which  the  phenomenon  of  interest  to  us 
occurs,  with  cases  in  which  it  does  not  occur,  we  seek 
to  rule  out  all  accidental  and  unessential  conjunctions. 
But  as  yet  nothing  has  been  said  of  quantitative  rela- 
tions. The  discovery  of  a  quantitative  agreement  or  cor- 
respondence between  two  phenomena,  or  two  groups  of 
phenomena,  often  enables  us  to  detect  a  causal  relation 
between  them  (cf.  pp.  192-193).  Moreover,  science  does 
not  rest  satisfied  with  the  mere  discovery  and  description 
of  changes,  and  the  order  in  which  they  occur.  We  may 
almost  say  that  science  does  not  exist  until  the  quanti- 
tative aspects  of  phenomena  are  taken  into  account  — 
until  things  are  weighed  and  measured.  The  physicist 
does  not  think  his  work  finished  when  he  has  proved 
that  sound  is  produced  by  atmospheric  vibrations.  He 
carries  on  his  analysis  until  he  can  discover  the  quanti- 
tative relations  between  the  amplitude  and  velocity  of 
the  vibrations,  and  the  loudness  and  pitch  of  the  result- 
ing tone.  And  the  psychologist  is  not  satisfied  with  the 
general  statement  that  certain  sensations  are  causally 
connected  with  certain  kinds  of  stimulus ;  but  he  seeks 
to  discover,  whenever  possible,  the  exact  quantitative 
relation  between  sensation  and  stimulus.  In  short,  the 


212  CAUSAL  DETERMINATION 

most  important  feature,  the  very  essence,  one  may  say, 
of  modern  scientific  investigation,  is  the  establishment 
of  quantitative  relations. 

Looking  at  two  things  from  the  standpoint  of  quan- 
tity, then,  we  say  that  when  their  variations  keep  pace 
with  each  other,  they  are  in  some  way  causally  con- 
nected. The  following  is  Mill's  statement  of  the  canon  : 
"  Whatever  phenomenon  varies  in  any  manner  whenever 
another  phenomenon  varies  in  a  particular  manner,  is 
either  a  cause  or  an  effect  of  that  phenomenon,  or  is  con- 
nected with  it  through  some  fact  of  causation"  The 
illustrations  of  this  law  given  by  Jevons  are  so  excellent 
that  we  cannot  do  better  than  adopt  them  :  — 

"The  illustrations  of  this  law  are  infinitely  numerous.  Thus 
Mr.  Joule,  of  Manchester,  conclusively  proved  that  friction  is  a  cause 
of  heat  by  expending  exact  quantities  of  force  by  rubbing  one  sub- 
stance against  another,  and  showed  that  the  heat  produced  was 
exactly  greater  or  less  in  proportion  as  the  force  was  greater  or  less. 
We  can  apply  the  method  to  many  cases  which  had  previously  been 
treated  by  the  simple  method  of  difference  ;  thus  instead  of  striking 
a  bell  in  a  complete  vacuum,  we  can  strike  it  with  a  very  little  air  in 
the  receiver  of  the  air-pump,  and  we  then  hear  a  very  faint  sound 
which  increases  or  decreases  every  time  we  increase  or  diminish  the 
density  of  the  air.  This  experiment  conclusively  satisfies  any  per- 
son that  air  is  the  cause  of  the  transmission  of  sound. 

"  It  is  this  method  which  often  enables  us  to  detect  the  material 
connection  which  exists  between  two  bodies.  For  a  long  time  it 
had  been  doubtful  whether  the  red  flames  seen  in  total  eclipses  of 
the  sun  belonged  to  the  sun  or  moon  ;  but  during  the  last  eclipse  of 
the  sun,  it  was  noticed  that  the  flames  moved  with  the  sun,  and  were 
gradually  covered  and  uncovered  by  the  moon  at  successive  instants 
of  the  eclipse.  No  one  could  doubt  thenceforth  that  they  belonged 
to  the  sun. 


§58.     THE   METHOD   OF   RESIDUES  213 

"Whenever,  again,  phenomena  go  through  Periodic  Changes,  alter- 
nately increasing  and  decreasing,  we  should  seek  for  other  phe- 
nomena which  go  through  changes  in  exactly  the  same  periods,  and 
these  will  probably  be  a  connection  of  cause  and  effect.  It  is  thus 
that  the  tides  are  proved  to  be  due  to  the  attraction  of  the  moon  and 
sun,  because  the  periods  of  high  and  low,  spring  and  neap  tides, 
succeed  each  other  in  intervals  corresponding  to  the  apparent  revo- 
lutions of  those  bodies  round  ,the  earth.  The  fact  that  the  moon 
revolves  upon  its  own  axis  in  exactly  the  same  period  that  it  revolves 
round  the  earth,  so  that  for  unknown  ages  past  the  same  side  of  the 
moon  has  always  been  turned  toward  the  earth,  is  a  most  perfect 
case  of  concomitant  variations,  conclusively  proving  that  the  earth's 
attraction  governs  the  motions  of  the  moon  on  its  own  axis. 

"  The  most  extraordinary  case  of  variations,  however,  consists  in 
the  connection  which  has  of  late  years  been  shown  to  exist  between 
the  Aurora  Borealis,  magnetic  storms,  and  the  spots  on  the  sun. 
It  has  only  in  the  last  thirty  or  forty  years  become  known  that  the 
magnetic  compass  is  subject  at  intervals  to  very  slight,  but  curious 
movements ;  and  that,  at  the  same  time,  there  are  usually  natural 
currents  of  electricity  produced  in  telegraph  wires,  so  as  to  interfere 
with  the  transmission  of  messages.  These  disturbances  are  known 
as  magnetic  storms,  and  are  often  observed  to  occur  when  a  fine  dis- 
play of  the  Northern  or  Southern  Lights  is  taking  place  in  some 
part  of  the  earth.  Observations  during  many  years  have  shown 
that  these  storms  come  to  their  worst  at  the  end  of  every  eleven 
years.  .  .  .  Close  observations  of  the  sun  during  thirty  or  forty  years 
have  shown  that  the  size  and  number  of  the  dark  spots,  which 
are  gigantic  storms  going  on  upon  the  sun's  surface,  increase  and 
decrease  exactly  at  the  same  periods  of  time  as  the  magnetic  storms 
upon  the  earth's  surface.  No  one  can  doubt,  then,  that  these  strange 
phenomena  are  connected  together,  though  the  mode  of  the  con- 
nection is  quite  unknown.  .  .  .  This  is  a  most  remarkable  and 
extensive  case  of  concomitant  variations."1 

§  58.   The  Method  of  Residues. — We  have  said  that 

1  Jevons,  Lessons  in  Logic,  pp.  249-251. 


214  CAUSAL  DETERMINATION 

modern  science  employs  measurement  whenever  possi- 
ble, in  order  to  determine  exactly  the  quantitative  rela- 
tions of  phenomena.  Groups  of  facts  whose  connections 
are  at  first  not  perceived,  or  at  best  but  vaguely  appre- 
hended, are  brought  into  close  relations  with  each  other 
by  the  establishment  of  definite  quantitative  relations. 
The  knowledge  that  electricity  possesses  energy,  for 
example,  is  very  vague  and  incomplete  when  compared 
with  the  definite  equations  which  the  physicist  can  fur- 
nish between  the  electrical  current  generated  under  cer- 
tain definite  conditions,  and  the  amount  of  work  which 
it  is  capable  of  performing.  But  the  discovery  of  quan- 
titative relations  not  only  renders  our  knowledge  more 
perfect  and  complete,  it  also  enables  us  in  some  cases  to 
detect  laws  of  connection  which  would  not  otherwise  be 
observed.  We  have  already  seen  how  the  perception  of 
corresponding  changes  in  the  quantities  of  phenomena 
has  led  to  the  discovery  of  causal  laws  by  means  of  the 
method  of  Concomitant  Variations.  The  method  of 
Residues,  which  we  now  have  to  discuss,  is  also  a  method 
of  quantitative  determination. 

In  general,  this  method  calls  attention  to  any  remain- 
der or  residue  which  is  left  over  after  other  portions  of 
a  complex  phenomenon  have  been  explained.  There  are 
two  results  of  this  method  which  may  be  discussed  sep- 
arately. 

(a)  The  application  of  this  method  to  a  complex 
phenomenon  which  is  the  result  of  several  causes, 
often  enables  us  to  determine  what  part  each  of  these 
causes  plays  in  the  determination  of  the  whole  fact 
under  consideration.  Mill's  fifth  canon  seems  to  apply 


§  58.    THE  METHOD   OF  RESIDUES  215 

to  this  case.  It  is  as  follows :  Subduct  from  any  phe- 
nomenon such  part  as  is  known  by  previous  inductions  to 
be  the  effect  of  certain  antecedents •,  and  the  residue  of  the 
phenomenon  is  the  effect  of  the  remaining  antecedents. 
Thus,  if  it  is  known  that  the  complex  phenomenon 
BAG  is  the  result  of  bac,  and  if  it  is  further  known 
that  a  is  the  cause  of  A,  and  b  of  B,  it  follows,  of  course, 
by  subtraction  that  the  residue  still  unexplained,  C,  is 
caused  by  c,  the  remaining  antecedent. 

Of  course  the  application  of  this  method  in  concrete  cases  does 
not  usually  resolve  itself  into  such  a  simple  process  of  subtraction. 
It  requires  work  — '  previous  inductions,1  as  Mill  says  —  to  deter- 
mine what  are  the  whole  number  of  antecedents  in  any  case,  as  well 
as  to  isolate  the  various  antecedents  so  as  to  determine  exactly  what 
part  of  the  effect  is  to  be  ascribed  to  each  one.  This  may  be  illus- 
trated by  an  example  :  after  my  student's  lamp  has  been  lighted  two 
hours,  I  find  the  thermometer  has  risen  from  65°  to  70°  Fahr.  The 
phenomenon  to  be  explained  then  is  the  additional  5°  of  heat. 
There  is  no  fire,  and  it  seems  that  the  increase  in  temperature  must 
be  due  to  the  lamp,  and  the  heat  given  off  from  my  body  during 
this  period.  Suppose  that  the  lamp  is  burned  for  the  same  length 
of  time  while  the  room  is  unoccupied,  all  other  conditions  remaining 
the  same,  and  that  the  thermometer  shows  an  increase  of  4°  in  the 
temperature.  By  subtraction  we  could  conclude  that  the  heat  given 
off  by  the  body  on  the  former  occasion  was  the  cause  of  the  additional 
degree  of  temperature. 

To  carry  the  process  of  analysis  a  step  further.  Let  us  suppose 
that  a  half  pint  of  oil,  which  is  composed  of  hydrogen  and  carbon, 
has  been  consumed.  We  could  determine,  by  measuring  the  heat 
produced  by  the  oxidation  of  the  exact  amount  of  carbon  contained  in 
one  half  a  pint  of  oil,  what  quantity  of  heat  is  due  to  the  combustion 
of  the  carbon  contained  in  the  oil,  and,  by  subtraction,  what  must  be 
ascribed  to  the  burning  of  the  hydrogen.1 

1  This  is,  of  course,  not  strictly  correct.  For  it  leaves  out  of  account  the 
heat  generated  by  the  chemical  combination  of  the  carbon  and  hydrogen. 
It  may  therefore  serve  to  illustrate  a  case  where  the  method  of  Residues 
breaks  down. 


2l6  CAUSAL  DETERMINATION 

(b)  The  second  case  in  which  this  method  may  be 
applied  is  where  there  is  an  unexplained  remainder  or 
residue  left  over  after  the  result  of  all  the  known  causes 
has  been  calculated.  Mill  does  not  distinguish  between 
such  instances  and  the  method  of  simple  subtraction 
discussed  above.  Since,  however,  the  cause  must  ex- 
plain the  whole  of  the  effect,  the  method  of  residues 
enjoins  us  to  continue  the  search  for  explanation. 
When  any  part  of  a  complex  phenomenon  is  still  un- 
explained by  the  causes  which  have  been  assigned,  a 
further  cause  for  this  remainder  must  be  sought.  If,  for 
example,  it  were  found  by  actual  measurement  that  the 
heat  produced  by  the  lamp,  and  by  the  body  of  the 
occupant,  were  not  sufficient  to  account  for  the  change 
in  temperature  of  the  room,  it  would  be  necessary  to 
seek  for  some  further  cause  to  account  for  this  unex- 
plained remainder. 

This  method  can  scarcely  be  said  to  be  more  than 
a  demand  for  complete  and  precise  explanation.  The 
attempt,  however,  to  account  for  unexplained  resi- 
dues has  led  to  many  extremely  important  discoveries 
in  science.  Residual  phenomena  are  often  so  obscure, 
and  appear  so  uninteresting  and  unimportant  to  the 
ordinary  mind,  that  they  are  passed  over  without  ex- 
planation. It  usually  requires  the  eye  of  a  scientific 
genius  to  see  the  importance  of  things  which  appear 
trivial  and  unessential.  With  Darwin,  facts  which  might 
appear  to  an  ordinary  observer  mere  unimportant  ex- 
ceptions, were  made  the  object  of  special  attention,  and 
often  served  as  starting-points  for  his  investigations. 
Francis  Darwin,  speaking  of  his  father,  says  :  "  There 
was  one  quality  of  mind  which  seemed  to  be  of  special 


§58.    THE  METHOD   OF   RESIDUES  217 

and  extreme  advantage  in  leading  him  to  make  discover- 
ies. It  was  the  power  of  never  letting  exceptions  pass 
unnoticed.  ...  A  point  apparently  slight  and  uncon- 
nected with  his  present  work  is  passed  over  by  many 
a  man  almost  unconsciously,  with  some  half-considered 
explanation,  which  is  really  no  explanation.  It  was  just 
these  things  that  he  seized  upon  to  make  a  start  from."  1 

Among  the  many  important  discoveries  which  have  resulted  from 
the  investigation  of  some  obscure  and  seemingly  unimportant  fact, 
we  may  mention  that  of  ozone.  It  had  been  observed  for  a  long 
time  that  the  passage  of  electric  sparks  through  the  air  is  accom- 
panied by  a  peculiar  odour.  This  odour  was  also  found  near 
electrical  machines,  and  was  known  as  the  ''  electrical  smell.1  No 
one  seemed  to  have  attached  any  importance  to  it  or  to  have  attempted 
to  explain  it  in  any  way,  until  Friedrich  Schbnbein,  a  professor  of 
chemistry  at  Basel,  turned  his  attention  to  the  subject.  The  result 
of  his  investigations  was  the  discovery  of  ozone,  the  peculiar  modifi- 
cation of  oxygen,  which  was  the  cause  of  the  odour. 

Another  very  striking  example  of  the  application  of  this  method 
is  afforded  by  the  history  of  the  discovery  of  the  planet  Neptune. 
In  1781  a  new  planet  was  discovered  moving  outside  all  the  other 
planets  by  Sir  William  Herschel.  This  was  the  planet  Uranus. 
When  its  orbit  came  to  be  calculated,  it  was  found  that  it  did  not 
move  as  it  might  be  expected  to  do  according  to  the  theory  of  gravi- 
tation. That  is,  the  attraction  of  the  sun  and  the  known  planets  did 
not  account  for  the  path  it  took :  it  moved  outwards  into  space 
further  than  it  ought  to  have  done.  It  was  evident  that  either  some 
mistake  must  have  been  made  in  the  observation  of  the  astronomers, 
or  some  unknown  body  must  be  dragging  it  out  of  its  course.  No 
traces  of  any  such  planet  could  be  perceived,  and  the  problem 
remained  unsolved.  In  1843,  a  student  of  St.  John's  College, 
Cambridge,  named  Adams,  undertook  to  work  out  the  movements 
of  Uranus,  to  discover,  if  possible,  the  position  of  the  body  which 

1  Life  and  Letters  of  Charles  Darwin,  Vol.  I.  p.  125. 


218  CAUSAL  DETERMINATION 

was  pulling  it  out  of  what  would  otherwise  be  its  proper  path,  the 
attractions  exercised  by  the  sun  and  the  planets  in  their  different 
positions,  and  to  show  what  effect  they  would  have  in  determining 
the  orbit  of  Uranus.  Whenever  the  planet  was  deflected  outwards, 
it  was  necessary  to  show  where  the  body  was  situated  which  was 
thus  influencing  it.  In  1845  he  was  able  to  send  a  paper  to  the 
astronomer  royal  at  Greenwich,  informing  him  in  what  quarter  of  the 
heavens  the  new  planet  should  be  observed.  When  the  discovery 
was  afterwards  made,  it  was  proved  that  his  calculations  were  almost 
exactly  correct.  A  failure  on  the  part  of  the  astronomer  royal  to 
cooperate  by  looking  through  his  telescope  for  the  planet  gave  the 
prior  right  of  discovery  to  a  Frenchman  named  Leverrier.  The 
latter  worked  out  his  calculations  in  the  same  way  as  Adams,  and 
obtained  almost  exactly  the  same  results.  He  sent  these  results  to 
Professor  Galle  of  the  Berlin  University  on  the  23d  September, 
1846,  asking  him  to  look  in  the  part  of  the  heavens  which  he 
indicated.  That  same  evening,  by  following  out  the  directions,  the 
planet  was  discovered  in  almost  the  exact  spot  predicted.1 

The  history  of  this  discovery  illustrates  as  well  several  methods 
and  processes  which  we  have  not  yet  discussed,  such  as  the  forma- 
tion and  verification  of  hypotheses.  It  is  also  interesting  as  showing 
how  reason  is  able  in  certain  conditions  to  anticipate  perception. 
The  relations  and  forces  of  the  heavenly  bodies  had  been  so  per- 
fectly formulated  in  the  law  of  gravitation  that  these  two  investi- 
gators, working  in  their  studies,  were  able  to  predict  not  only  the 
presence  but  the  exact  position  of  a  planet  which  up  to  that  time  had 
never  been  observed. 

In  connection  with  Chapters  XV.  and  XVI.,  the  student  is  ad- 
vised to  read  Mill,  Logic,  Bk.  III.  Chs.  VIII.  and  IX. 

1  Cf.  Clerke,  A  Popular  History  of  Astronomy  during  the  Nineteenth 
Century,  pp.  96  ff.  ;  Buckley,  A  Short  History  of  Natural  Science,  pp. 
302  ff. 


CHAPTER   XVII 

METHODS    OF    EXPLANATION 

Incomplete  Explanation. — Analogy 

§  59.  Explanation  by  Analogy.  —  We  have  now  passed 
from  the  field  of  observation  to  that  of  explanation. 
Scientific  observation,  aided  by  experiment,  as  we  have 
seen,  has  to  determine  the  exact  nature  of  the  facts  of 
experience,  and  the  order  in  which  those  facts  are  con- 
nected. Explanation,  on  the  other  hand,  undertakes  to 
furnish  reasons  why  the  facts  are  as  we  find  them  to  be. 
But,  as  has  already  been  pointed  out  (§§  48,  49),  no  hard 
and  fast  line  can  be  drawn  between  the  determination 
of  the  nature  and  connection  of  facts,  and  their  explana- 
tion. The  task  which  our  thought  is  called  upon  to 
perform  is  to  transform  obscurely  known  and  isolated 
facts  into  an  orderly  and  consistent  system  of  know- 
ledge. And,  to  accomplish  this,  it  is  necessary,  in  the 
first  place,  that  the  facts  shall  be  thoroughly  analyzed 
and  carefully  examined;  and,  secondly,  that  they  shall 
be  grouped  together  according  to  some  general  principle 
or  principles  which  shall  make  clear  and  intelligible  the 
relations  in  which  they  stand  to  each  other. 

To  explain,  then,  is  just  to  show  that  some  fact  or 
group  of  facts  is  related  to  some  other  fact  or  group  with 
which  we  are  acquainted.  So  far  as  the  methods  we  have 

219 


220  ANALOGY 

discussed  enable  us  to  establish  connections  between 
events,  they  may  fairly  claim  to  be  methods  of  explana- 
tion. Nevertheless,  although  the  difference  between 
these  methods  and  those  of  explanation  proper  is  one  of 
degree  rather  than  of  essential  nature,  it  is  important  to 
keep  it  in  mind.  The  canons  which  were  stated  in  the 
last  two  chapters  —  what  Mill  named  the  experimental 
methods  —  are  rules  for  determining  the  order  and 
succession  of  particular  facts.  The  problem  before  us 
in  those  chapters  was  to  determine  what  particular 
phenomena  of  our  experience  are  essentially  and  neces- 
sarily connected  as  antecedents  and  consequents.  And 
for  this  purpose  active  observation,  aided  by  experi- 
ment, suffices.  It  is,  of  course,  true  that  these  observa- 
tions and  experiments  furnish  the  starting-point  for 
explanation.  But  they  constitute  a  more  or  less  distinct 
step  in  the  work  of  systematization  which  is  carried  on  by 
thought.  The  method  of  Difference,  for  instance,  enables 
us  to  say  that  hot  water  will  break  thick  glasses  when 
poured  into  them,  but  will  not  injure  thin  ones.  '  So 
much  for  the  fact?  we  say,  'but  the  explanation  is  still 
wanting.'  We  must  try  to  make  the  fact  intelligible  by 
going  outside  of  it,  and  showing  that  this  behaviour  on 
the  part  of  the  glasses  is  simply  a  case  or  illustration  of 
what  we  already  know  of  the  properties  of  bodies  when 
heated.  Again,  the  method  of  Concomitant  variations, 
as  we  have  seen  from  Jevons's  example,  has  led  us  to 
believe  in  some  causal  connection  between  electrical 
storms,  sun-spots,  and  the  Aurora  Borealis.  In  this 
instance,  knowledge  has  not  been  able  to  advance 
beyond  the  fact  to  its  explanation.  No  satisfactory 


§59-     EXPLANATION  BY  ANALOGY  221 

theory  has  yet  been  established  to  account  for  the 
undoubted  fact  that  these  phenomena  are  in  some  way 
causally  connected. 

In  discussing  methods  of  Explanation,  we  deal  first 
with  Analogy.  The  principle  of  Analogy  is  resem- 
blance. The  phenomenon  to  be  explained  is  connected 
with  some  more  familiar  occurrence  through  some 
perceived  or  imagined  likeness  between  the  two,  cases. 
In  the  early  stages  of  the  history  of  the  race,  everything 
was  explained  on  the  analogy  of  human  actions  (cf.  §  84). 
All  natural  events,  that  is,  were  supposed  to  be  produced 
by  superhuman  agents,  who  were,  however,  endowed 
with  essentially  the  same  qualities  as  man.  In  the 
thunder,  the  men  of  a  primitive  age  heard  the  voice  of  a 
god.  An  eclipse  of  the  sun  or  moon  was  interpreted  as 
a  divine  sign  or  warning.  When  the  sea  became  tem- 
pestuous and  lashed  its  shores,  they  believed  that  the 
sea-god  was  angry.  In  every  case,  they  interpreted 
these  mysterious  happenings  of  nature  by  referring 
them  to  causes  similar  in  character  to  those  which  they 
best  understood  —  the  motives  and  volitions  of  them- 
selves and  their  fellows. 

The  principle  of  analogy  is  employed  in  the  same 
way  in  modern  times.  It  is  true  that  we  no  longer 
think  that  natural  events  are  directly  caused  by  the 
action  of  some  spiritual  agent  more  or  less  like  our- 
selves. But,  when  we  endeavour  to  show  that  the  phe- 
nomena which  we  are  interested  to  explain  are  similar 
in  important  respects  to  some  group  of  facts  with  whose 
mode  of  operation  we  are  familiar,  we  proceed  by  anal- 
ogy. On  the  basis  of  this  similarity,  we  argue  that  the 


222  ANALOGY 

phenomena  with  which  we  are  dealing  probably  have 
the  same  properties,  or  operate  in  the  same  way,  or  are 
governed  by  the  same  laws,  as  the  better-known  facts 
which  they  resemble.  The  formula  of  analogy  may 
be  stated  in  this  way :  Two  things  resemble  each 
other  in  one  or  more  respects,  they  are  therefore  of 
the  same  general  type  or  character;  therefore  a  cer- 
tain proposition  which  is  true  of  the  one  is  probably 
true  of  the  other.  The  following  example  of  analogy 
has  been  frequently  used  as  an  illustration  :  — 

"We  may  observe  a  very  great  similitude  between  this  earth 
which  we  inhabit,  and  the  other  planets,  Saturn,  Jupiter,  Mars, 
Venus,  and  Mercury.  They  all  revolve  round  the  sun,  as  the  earth 
does,  although  at  different  distances  and  in  different  periods.  They 
borrow  all  their  light  from  the  sun,  as  the  earth  does.  Several  of 
them  are  known  to  revolve  around  their  axes  like  the  earth,  and  by 
that  means  must  have  a  like  succession  of  day  and  night.  Some  of 
them  have  moons  that  serve  to  give  them  lignt  in  the  absence  of  the 
sun,  as  our  moon  does  to  us.  They  are  all  in  their  motions  subject 
to  the  same  law  of  gravitation  as  the  earth  is.  From  all  this  simili- 
tude, it  is  not  unreasonable  to  think  that  those  planets  may,  like  our 
earth,  be  the  habitation  of  various  orders  of  living  creatures."  1 

The  word  i  analogy '  at  the  present  time  is  somewhat  loosely  used 
for  any  mark  of  similarity  or  resemblance  which  enables  us  to  rea- 
son from  one  thing  to  another.  "The  original  word  di/oAoyi'ji, 
as  employed  by  Aristotle,  corresponds  to  the  word  Proportion  in 
Arithmetic  ;  it  signifies  an  equality  of  ratios,  icrdrrys  Ao'yeov  :  two 
compared  with  four  is  analogous  to  four  compared  with  eight. 
There  is  something  of  the  same  meaning  in  the  technical  use  of  the 
word  in  physiology,  where  it  is  used  to  signify  similarity  of  function  as 
distinguished  from  similarity  of  structure,  which  is  called  homology ; 
thus  the  tail  of  a  whale  is  analogous  to  the  tail  of  a  fish,  inasmuch 

1  Reid,  Intellectual  Powers  of  Man,  Essay  I.  Chap.  &i» 


§  60.    ANALOGY  AS   SUGGESTIVE  OF  HYPOTHESES     223 

as  it  is  similarly  used  for  motion,  but  is  homologous  with  the  hind- 
legs  of  a  quadruped.  A  man's  arms  are  homologous  with  a  horse's 
fore  legs,  but  they  are  not  analogous,  inasmuch  as  they  are  not  used 
for  progression.1'1 

Apart  from  these  technical  uses,  what  is  known  as 
analogical  reasoning  may,  perhaps,  be  best  defined  as 
an  argument  from  similar  instances.  In  analogy,  we  do 
not  stop  to  work  out  a  law  of  connection  between 
phenomena  by  comparing  a  number  of  cases,  or  by 
using  any  of  the  ordinary  inductive  canons.  But 
finding  a  striking  resemblance  between  some  circum- 
stance—  quality,  arrangement,  function,  etc. — in  the 
phenomena  to  be  explained,  and  some  phenomena  with 
which  we  are  already  acquainted,  we  used  the  latter  as 
a  basis  for  conclusions  about  the  former.  Analogy  is 
thus  an  argument  from  examples  or  instances,  its  value 
depending  upon  the  real  identity  in  some  important 
aspect  of  the  cases  compared.  When,  however,  our 
thought  is  able  to  extend  to  a  new  case,  or  set  of 
cases,  some  general  law  or  principle  with  whose  opera- 
tion it  is  already  acquainted  in  other  instances,  we  have 
passed  beyond  analogy  to  complete  explanation.  In 
the  former  case,  we  argue  from  the  resemblance  of 
instances ;  in  the  latter,  the  thread  which  binds  the 
new  instance  with  the  old  is  the  identity  of  a  general 
principle. 

§  60.   Analogy  as  Suggestive  of  Explanatory  Hypothe- 
ses. —  We  have  shown  above  that  analogical  reasoning 

1  Minto,  Logic  Inductive  and  Deductive,   p.  367. 


224  ANALOGY 

depends  on  the  resemblance  which  exists  between  indi- 
vidual cases  or  instances,  and  that  it  is  not  guided  by 
any  general  law  or  principle.  In  the  next  section,  how- 
ever, we  propose  to  show  in  more  detail  wherein  it  falls 
short,  and  why,  taken  by  itself,  it  can  only  be  regarded 
as  incomplete  explanation.  Here  we  have  to  notice  the 
important  part  which  it  plays  in  suggesting  laws  and 
principles.  Although  analogy  '  sticks  in  the  particular 
instances,'  it  leads  the  mind  on  to  general  laws  and 
explanatory  theories.  It  is  thus  of  the  greatest  impor- 
tance as  a  necessary  stage  on  the  way  to  complete 
explanation.  * 

When  we  are  able  to  discover  some  general  resem- 
blance between  a  group  of  phenomena  which  we  are  in- 
terested to  explain,  and  another  group  whose  principle  of 
operation  we  already  understand,  our  thought  strives  to 
extend  the  known  principle  and  to  bring  the  new  facts 
under  it.  The  unknown  or  unexplained  facts  are  thus 
brought  under  a  known  law.  It  is  of  course  true  that 
the  application  of  the  law  to  a  new  set  of  facts  broadens 
our  conception  of  its  scope,  and  often  requires  us  to  state 
it  in  a  more  adequate  way.  Thus  the  analogy  which 
Newton  perceived  between  the  heavenly  bodies  falling 
through  space  and  the  falling  of  the  apple  towards  the 
ground,  led  to  the  formulation  in  exact  mathematical 
terms  of  the  universal  law  of  gravitation.  Our  know- 
ledge of  the  various  functions  of  plants  —  digestion,  re- 
production, etc.  —  has  been  obtained  by  ascribing  to  the 
various  organs  of  the  plant,  purposes  analogous  to  those 
which  are  fulfilled  by  the  parts  of  animal  bodies.  And, 
in  turn,  the  study  of  plant  physiology  has  thrown  light 


§  6o.     ANALOGY   AS    SUGGESTIVE   OF   HYPOTHESES     225 

upon  animal  physiology,  and  enlarged  and  modified  many 
of  its  theories. 


An  extremely  interesting  instance  of  the  part  which  analogy 
plays  in  suggesting  possible  explanations,  is  found  in  the  account 
of  the  discovery  of  the  principle  of  Natural  Selection  given  by  Dar- 
win in  his  Autobiography.  In  1837  Darwin  opened  a  note-book 
for  the  purpose  of  recording  all  facts  in  any  way  connected  with  the 
variation  of  species  in  nature  and  under  domestication.  He  first 
investigated  the  variations  of  plants  and  animals  which  are  produced 
under  domestication,  by  printed  enquiries,  by  conversation  with 
skilful  breeders,  and  by  extensive  reading.  "  I  soon  found,1'  he  says, 
"  that  selection  was  the  keystone  of  man's  success  in  making  useful 
races  of  plants  and  animals."  When  useful  or  pleasing  varieties 
of  plants  or  animals  occur,  the  gardener  or  breeder  preserves  them, 
and  their  peculiar  qualities  are  transmitted  to  their  offspring.  And, 
in  a  number  of  generations,  these  qualities  become  more  pronounced 
through  accumulation.  The  differences  between  varieties  of  the 
same  species  of  domesticated  animals  —  varieties  which  are  as  differ- 
ent, for  example,  as  the  mastiff  and  Skye  terrier  —  are  due  to  the 
selective  agency  of  man.  But  is  there  anything  analogous  takes 
place  on  an  indefinitely  larger  scale  in  nature  ?  If  so,  what 'is  it 
which  plays  the  part  of  the  gardener  or  breeder,  and  preserves  cer- 
tain varieties  ? 

When  Darwin  had  reached  this  point  in  his  investigations,  and 
had  come  to  appreciate  what  selection  could  do,  he  happened  to 
read  Malthus's  book,  On  Population.  The  purpose  of  this  book 
was  to  dispel  the  optimistic  ideas  of  some  of  the  writers  of  the 
eighteenth  century  who  looked  for  the  speedy  realization  of  social 
well-being  and  happiness.  Such  an  ideal  is  impossible  of  fulfilment, 
said  Malthus,  because  of  the  inevitable  tendency  of  population  to 
increase  faster  than  the  supply  of  food.  Human  beings  increase  in 
a  geometrical  ratio ;  the  means  of  subsistence,  at  best,  only  by  an 
arithmetical  ratio.  The  population  will  thus  constantly  tend  to 
exceed  the  limit  of  the  food  supply,  and  will  be  kept  in  check  only 
by  starvation.  A  constant  struggle  for  food  is  the  lot,  then,  to 
Q 


226  ANALOGY 

which  each  individual  is  doomed  in  virtue  of  this  law.  Darwin's 
observations  of  the  rate  at  which  plants  and  animals  tend  to  repro- 
duce their  kind,  led  him  at  once  to  extend  Malthus's  principle  to 
the  whole  of  nature.  The  fecundity  of  natural  beings  leads  to  a 
struggle  for  existence,  not  merely  among  men,  but  throughout  the 
whole  organic  world.  And  if  there  is  a  struggle,  we  have  natural 
selection  or  the  survival  of  the  fittest.  Darwin  saw  "  that  natural 
selection  was  the  inevitable  result  of  the  rapid  increase  of  all  organic 
beings."  It  is  not  difficult  to  see  that  this  discovery  was  the  result 
of  Darwin's  wonderful  power  of  perceiving  analogies  between  differ- 
ent classes  of  facts.  His  genius  led  him  to  recognize  first  the  re- 
semblance of  the  variations  of  species  in  nature,  to  the  more  familiar 
variations  which  go  on  among  domesticated  plants  and  animals. 
And,  secondly,  he  perceived  that  the  competition  for  the  means  of 
subsistence,  which  the  pressure  of  population  imposes  upon  the  mem- 
bers of  the  human  race,  is  simply  one  phase  of  ( the  struggle  for 
existence,1  which  is  going  on  everywhere  throughout  the  organic 
world. 

§  61.    The  Incompleteness  of  Analogical  Reasoning. — 

The  most  striking  feature  of  analogical  arguments  is 
found  in  the  fact  that  they  yield  only  probable  conclu- 
sions. And  the  reason  for  this  is  not  far  to  seek.  For, 
as  has  been  already  shown,  analogy  is  a  method  of 
reasoning  from  one  particular  case  to  another  on  the 
basis  of  some  imagined  or  perceived  similarity  between 
the  two  cases.  Complete  logical  demonstration,  or  cer- 
tainty, however,  is  attained  only  when  the  new  fact  or 
group  of  facts  is  really  and  essentially  united  by  means 
of  some  general  principle  with  what  is  already  known. 

But  it  must  not  be  forgotten  that  '  probability '  is  not 
a  fixed  quantity.  An  argument  from  analogy  may  have 
any  degree  of  value,  from  zero  almost  up  to  the  limit 
of  complete  logical  certainty.  To  fully  explain  or 


§  6i.     INCOMPLETENESS  OF  ANALOGICAL   REASONING     227 

demonstrate  any  fact,  we  are  obliged,  I  think,  to  go 
beyond  analogy,  and  to  verify  its  conclusions  by  a 
method  which  has  still  to  be  described.  It  is  evident, 
nevertheless,  that  the  value  of  an  analogical  argument 
will  depend  upon  the  nature  of  the  resemblance  which 
is  taken  as  the  basis  of  inference.  In  general,  it  is 
true  that  the  greater  the  resemblance  between  the  two 
cases,  the  more  certainly  can  we  reason  from  one  to  the 
other.  This  is  not  to  say,  however,  that  the  value  of 
the  conclusion  is  in  direct  proportion  to  the  number 
of  points  of  resemblance  which  can  be  discovered.  For 
example,  we  might  reason  :  These  two  men  are  of  the 
same  height,  of  the  same  age,  live  in  the  same  house, 
come  from  the  same  town  ;  the  one  man  stands  well 
in  his  classes,  therefore  the  other  probably  does  so  also. 
If  the  mtmber  of  points  of  resemblance  were  the  essen- 
tial thing,  the  argument  ought  to  possess  some  weight, 
but  it  is  clear  that  it  has  none.  The  difficulty  is  that 
none  of  the  resemblances  mentioned  are  fundamental, 
or  in  any  way  essential  to  the  real  nature  of  the  things 
compared.  If  we  knew  that  the  two  men  were  similar 
in  character,  this  one  characteristic  would  be  worth 
more,  as  a  basis  for  the  conclusion,  than  all  the  circum- 
stances which  we  have  mentioned  combined. 

It  is  true,  then,  as  Mr.  Bosanquet  remarks,  that  in 
analogical  reasoning  we  must  weigh  the  points  of  re- 
semblance rather  than  count  them.1  Other  things 
being  equal,  the  more  points  of  resemblance  we  can 
make  out  the  better;  but  if  these  are,  to  contribute  at 

i  Logic,  Vol.  II.,  p.  99, 


228  ANALOGY 

all  to  the  certainty  of  the  conclusion,  they  must  rep- 
resent some  deep-lying  characteristic  of  the  things 
compared.  In  general,  it  must  be  said  that  it  is  only 
experience  which  can  inform  us  what  resemblances  are 
fundamental,  and  what  merely  external.  Systematic 
knowledge  in  any  field  enables  us  to  separate  the  essen- 
tial from  the  accidental.  And,  what  is  perhaps  a  corol- 
lary from  this,  it  must  not  be  forgotten  that  the  value 
of  an  inference  from  analogy  depends  largely  upon  the 
amount  of  intellectual  insight  possessed  by  the  mind 
which  makes  it.  The  ordinary  mind,  at  least  in  its 
undisciplined  and  untutored  condition,  regards  all  things 
as  of  equal  importance.  It  is  therefore  led  away  by 
the  strongest  stimulus  —  by  striking  external  and  acci- 
dental resemblances.  On  the  other  hand,  a  scientific 
genius  whose  mind  is  well  stored  with  facts,  and  who 
is  gifted  in  addition  with  imagination,  is  able  to  pene- 
trate beneath  the  surface  and  to  apprehend  the  real  or 
fundamental  resemblance.  His  imagination  enables 
him  to  see  beyond  the  chaos  of  the  particular  facts, 
and  to  detect  the  underlying  principle  by  means  of 
which  these  facts  can  be  connected  and  systema- 
tized. 

Analogy  thus  becomes  deepened  until  it  passes  from 
the  stage  of  a  mere  argument  from  particular  to  par- 
ticular, to  the  perception  of  a  general  law  which  includes 
the  individual  instance.  But  no  such  direct  insight  can 
claim  the  title  of  knowledge,  until  it  is  tried  and  tested 
by  the  facts.  The  guesses  of  scientific  men  unfortu- 
nately often  prove  mistaken.  It  is  always  necessary 
that  fancy  shall  be  confronted  with  facts.  Even  Dar- 


§  6i.     INCOMPLETENESS   OF  ANALOGICAL   REASONING    229 

win's  magnificent  analogical  inference  was  nothing 
more  than  a  hypothesis,  as  he  himself  well  under- 
stood, until  its  power  of  explaining  the  facts  of  organic 
life  was  demonstrated.  We  have  now  to  explain  in 
the  next  chapter  the  methods  by  which  such  guesses 
are  tested. 

References 

J.  S.  Mill,  Logic,  Bk.  III.  Ch.  XX. 

A.  Bain,  Logic,  Part  Second,  Induction,  pp.  140-1480 
J.  G.  Hibben,  Inductive  Logic,  Ch.  XIV. 

B.  Bosanquet,  Logic,  Vol.  II.  Ch.  III. 

"          "  The  Essentials  of  Logic,  pp.  155-158. 

W.  Minto,  Logic  Inductive  and  Deductive,  pp.  367-373. 


CHAPTER   XVIII 

METHODS    OF    EXPLANATION. THE    USE   OF   HYPOTHESES 

§  62.  Reasoning  from  an  Hypothesis.  —  An  hypothesis 
is  a  guess  or  supposition  made  to  explain  some  fact  or 
group  of  facts.  We  have  seen  in  the  last  chapter  how 
the  mind  is  led  on  by  the  perception  of  analogies  to 
formulate  a  general  law  or  principle  of  explanation  for 
phenomena  which  were  not  previously  understood.  But 
even  when  guided  by  analogy,  a  guess  or  hypothesis  is 
only  the  beginning  of  explanation.  A  mere  hypothesis 
or  supposition  must  be  tried  by  its  capacity  to  explain 
facts,  and  in  this  way  either  verified  or  disproved. 
'  Theory  '  is  another  word  that  is  often  used  as  equiva- 
lent to  hypothesis.  Strictly  speaking,  however,  it  is 
more  correct  to  use  the  term  '  hypothesis  '  for  the  un- 
verified, or  only  partially  verified  guess,  and  to  reserve 
1  theory'  for  the  hypothesis  that  has  been  more  com- 
pletely demonstrated.  This  distinction,  however,  is  not 
usually  maintained,  and  even  in  scientific  writings  the 
terms  '  theory  '  and  *  hypothesis  '  are  used  interchangea- 
bly. Nevertheless,  it  is  necessary  to  distinguish  in  some 
way  the  '  mere  hypothesis,'  or  supposition,  which  is 
quite  as  likely  to  be  false  as  true,  from  the  hypothesis 
which  has  been  established  by  proof. 

It  is  well  to  remember  that  it  is  not  only  in  solving 
scientific  problems  that  we  employ  hypotheses.  In  our 

230 


Co 


5' 


§62.     REASONING   FROM   AN   HYPOTHESIS  231 

ordinary  experience,  we  are  constantly  trying  to  imagine 
the  most  likely  explanation  of  facts  which  we  perceive 
through  the  senses.  If,  for  example,  one  should  find  on 
returning  to  one's  room  that  a  pane  of  glass  had  been 
broken,  one  would  straightway  set  about  finding  some 
explanation  of  this  occurrence.  One  might  perhaps 
first  imagine  that  a  stone  or  something  of  the  kind  had 
been  thrown  against  it.  Acting  on  this  supposition,  one 
would  look  for  the  stone  in  the  room.  If  it  were  found 
there,  the  hypothesis  would  be  confirmed  ;  if  no  traces  of 
it  could  be  discovered,  and  if,  moreover,  on  examination 
the  glass  proved  to  be  shattered  in  a  way  that  would 
probably  not  result  from  the  projection  of  a  stone 
against  it,  our  first  hypothesis  would  have  to  be  aban- 
doned. We  should  then  make  another  guess  —  perhaps 
that  the  outside  blind  had  been  violently  closed  by  the 
wind  —  and  again  examine  the  facts  to  see  if  they  gave 
any  support  to  this  supposition.  We  are  constantly 
making  hypotheses  of  this  character  to  explain  phe- 
nomena which  we  meet  with  in  everyday  experience. 
If  we  find  a  stream  swollen,  we  conclude  that  it  must 
have  rained  in  some  part  of  the  country  drained  by 
the  stream.  If  a  man  has  typhoid  fever,  we  are  pretty 
sure  to  guess  that  he  has  been  drinking  impure  water. 
We  no  sooner  perceive  something  unusual  or  striking 
than  we  begin  to  guess  out,  as  it  were,  its  explanation. 
The  formation  of  hypotheses,  then,  is  simply  the  mind's 
response  to  the  demand  for  explanation. 

It  is  worth  noticing  that  it  is  only  unusual  or  striking  events,  or 
those  in  which  they  have  some  practical  concern,  which  attract  the 
attention  of  the  majority  of  mankind,  and  lead  them  to  form  explana- 


232  THE  USE  OF   HYPOTHESES 

tory  hypotheses.  What  is  familiar,  or  of  no  practical  importance, 
does  not  usually  awaken  curiosity.  Indeed,  in  a  great  many  cases, 
such  phenomena  are  not  observed  at  all.  But  the  great  scientist  is 
distinguished,  one  may  say,  by  his  intellectual  curiosity.  He  tries 
to  understand  phenomena  which  the  ordinary  mind  neglects,  and 
simply  takes  for  granted.  He  has  questions  in  his  mind  with  regard 
to  familiar  things  which  he  wishes  to  have  answered,  guesses  which 
he  is  desirous  of  having  proved  or  disproved.  We  have  found  it 
convenient,  in  the  preceding  chapters,  to  separate  the  description  of 
the  processes  of  determining  the  nature  of  facts,  from  the  account 
of  the  methods  of  explanation.  But  it  must  by  no  means  be  sup- 
posed that  the  nature  of  facts  is  discovered  quite  independently  of 
the  influence  of  hypotheses  or  theories.  Unless  the  mind  has 
some  question  to  answer,  or  theory  to  test,  it  is  impossible  to  see 
any  significance  in  an  experiment.  In  other  words,  every  ex- 
periment must  have  a  purpose,  and  the  purpose  is  to  get  some 
information  that  will  help  us  to  answer  a  question  which  we  bring 
with  us  to  the  investigation. 

In  the  actual  process  of  acquiring  knowledge,  then, 
observation  and  theorizing  go  hand  in  hand.  Unless  we 
go  to  nature  with  something  in  our  mind,  we  are  not 
likely  to  learn  much.  As  a  rule,  we  see  only  what  we 
look  for.  Francis  Darwin  says  of  his  father :  "  He 
often  said  that  no  one  could  be  a  good  observer  unless 
he  were  an  active  theorizer.  This  brings  me  back  to 
what  I  said  about  his  instinct  for  arresting  exceptions : 
It  were  as  though  he  were  charged  with  theorizing 
power  ready  to  flow  into  any  channel  on  the  slightest 
disturbance,  so  that  no  fact,  however  small,  could  avoid 
releasing  a  stream  of  theory,  and  thus  the  fact  became 
magnified  into  importance.  In  this  way  it  naturally 
happened  that  many  untenable  theories  occurred  to  him, 
but  fortunately  his  richness  of  imagination  was  equalled 


§  62,     REASONING   FROM   AN   HYPOTHESIS  233 

by  his  power  of  judging  and  condemning  the  thoughts 
which  occurred  to  him.  He  was  just  to  his  theories  and 
did  not  condemn  them  unheard ;  and  so  it  happened 
that  he  was  willing  to  test  what  would  seem  to  most 
people  not  at  all  worth  testing.  These  rather  wild  trials 
he  called  '  fool's  experiments,'  and  enjoyed  exceedingly. 
As  an  example,  I  may  mention,  that  finding  the  cotyle- 
dons of  Biophytum  to  be  highly  sensitive  to  vibrations 
of  the  table,  he  fancied  that  they  might  perceive  the 
vibrations  of  sound,  and  therefore  made  me  play  my 
bassoon  close  to  a  plant."  l 

A  good  example  of  how  essential  theories  are  for  an 
observer,  and  how  blind  he  may  be  to  what  he  is  not 
looking  for,  is  found  in  the  work  from  which  we  have 
just  quoted.  In  the  brief  autobiography  contained  in 
the  first  volume,  Darwin  tells  of  a  geological  trip  through 
Wales  which  he  took  while  a  student  at  Cambridge,  in 
company  with  Sedgwick,  the  professor  of  geology.  It 
must  be  remembered  that  this  was  before  Agassiz  had 
come  forward  with  his  theory  of  a  glacial  period  in  the 
world's  history.  Darwin  writes :  "  We  spent  many 
hours  in  Cwm  Idwal,  examining  all  the  rocks  with  su- 
preme care,  as  Sedgwick  was  anxious  to  find  fossils  in 
them ;  but  neither  of  us  saw  a  trace  of  the  wonderful 
glacial  phenomena  all  around  us ;  we  did  not  notice  the 
plainly  scored  rocks,  the  perched  boulders,  the  lateral 
and  terminal  moraines.  Yet  these  phenomena  are  so 
conspicuous  that,  as  I  declared  in  a  paper  published 
many  years  afterward  in  the  Philosophical  Magazine,  a 

lLife  and  Letters  of  Charles  Darwin,  Vol.  I.,  p.  126. 


234  THE  USE  OF  HYPOTHESES 

house  burnt  down  by  fire  did  not  tell  its  story  more 
plainly  than  did  this  valley.  If  it  had  been  filled  by  a 
glacier,  the  phenomena  would  have  been  less  distinct 
than  they  now  are."  l 

§  63.  Formation  of  Hypotheses.  —  We  are  now  ready  to 
consider  a  little  more  closely  the  formation  of  hypothe- 
ses or  theories.  In  the  first  place,  it  is  to  be  noticed 
that  hypotheses  are  not  received  from  without  through 
sense-perception,  but  are  made  by  the  mind.  They  are 
the  creations  of  the  imagination.  A  good  theorizer,  like 
a  poet,  is  in  a  certain  sense  born,  not  made.  The  man 
to  whom  '  nothing  ever  occurs,'  whose  intellectual  pro- 
cesses are  never  lit  up  with  a  spark  of  imagination,  is 
unlikely  to  make  any  important  discoveries.  It  has 
been  by  a  flash  of  scientific  genius,  by  imaginative  in- 
sight which  we  may  almost  call  inspiration,  that  great 
scientific  theories  have  been  discovered.  Not  even  a 
scientific  genius,  however,  can  afford  to  neglect  the 
facts.  But,  guided  by  accurate  observation,  the  scien- 
tific imagination  tries  to  invent  some  law  or  principle 
which  will  serve  to  connect  and  explain  facts.  Tyndall 
has  an  essay  on  "  The  Scientific  Use  of  the  Imagina- 
tion," from  which  we  may  quote  a  short  passage. 
"With  accurate  experiment  and  observation  to  work 
upon,  imagination  becomes  the  architect  of  physical 
theory.  Newton's  passage  from  a  falling  apple  to  a 
falling  moon  was  an  act  of  the  prepared  imagination. 
.  .  .  Out  of  the  facts  of  chemistry  the  constructive 

1  Life  and  Letters  of  Charles  Darwin^  Vol.  I.,  p.  49. 


§  63.     FORMATION  OF   HYPOTHESES  235 

imagination  of  Dalton  formed  the  atomic  theory.  Davy 
was  richly  endowed  with  the  imaginative  faculty,  while 
with  Faraday  its  exercise  was  incessant,  preceding, 
accompanying,  and  guiding  all  his  experiments.  His 
strength  and  fertility  as  a  discoverer  are  to  be  referred 
in  great  part  to  the  stimulus  of  the  imagination.  Scien- 
tific men  fight  shy  of  the  word  because  of  its  ultra- 
scientific  connotations ;  but  the  fact  is,  that  without  the 
exercise  of  this  power,  our  knowledge  of  nature  would 
be  a  mere  tabulation  of  coexistences  and  sequences."1 

In  speaking  of  hypotheses  as  '  guesses,'  or  l  creations  of  the  im- 
agination,' their  dependence  upon  facts  must  not  be  forgotten.  It  is 
only  when  the  phenomena  to  be  explained  have  been  carefully  ob- 
served that  our  guesses  at  their  explanation  are  likely  to  be  of  value. 
It  is  well  known  that  a  considerable  amount  of  knowledge  is  usually 
required  to  ask  an  intelligent  question.  And  in  the  same  way,  the 
mind  must  be  well  stored  with  facts,  in  order  to  render  our  hypo- 
thetical explanations  worthy  of  consideration.  Indeed,  observation 
of  facts,  and  the  formation  of  theories  go  hand  in  hand,  and  naturally 
assist  each  other.  We  have  already  spoken  of  the  lack  of  theory 
which  makes  us  blind  to  facts  which  seem  to  lie  directly  before  us. 
But  we  have  perhaps  not  yet  emphasized  sufficiently  the  dependence 
of  theories  upon  the  facts  of  observation.  The  process  of  explanation 
may  be  described  as  a  fitting  together  of  the  facts  given  by  observa- 
tion, with  the  explanatory  theories  which  the  mind  originates.  The 
theory  with  which  we  start  enables  us  to  ask  questions,  and  leads  us 
to  scrutinize  the  phenomena  which  are  to  be  explained ;  while  the 
latter  react  upon  the  theory,  and  cause  it  to  undergo  constant  modifi- 
cation. The  account  of  Darwin's  discovery  of  the  principle  of  *  the 
survival  of  the  fittest '  is  a  good  illustration  of  an  hypothesis  con- 
structed by  a  constant  dependence  upon  the  facts  during  every  step 
of  its  progress. 

^Fragments  of  Science,  p.  104. 


236  THE  USE  OF   HYPOTHESES 

We  have  already  referred  to  the  way  in  which  analogy 
leads  the  mind  on  to  general  principles  of  explanation 
(§  60).  Analogy  is  a  method  of  inferring  that  what  is 
true  of  one  object  is  probably  true  of  others  which 
resemble  it.  But  the  ordinary  mind  sees  resemblances 
only  when  they  are  very  obvious  and  striking.  The  man 
of  scientific  insight,  on  the  other  hand,  like  the  poet,  pene- 
trates more  deeply  into  the  nature  of  things,  and  is  able 
to  discover  analogies  and  resemblances  to  which  the 
ordinary  man  is  blind.  Who  but  a  genius  like  Newton 
would  have  thought  of  connecting  the  fall  of  an  apple 
with  the  fall  of  the  heavenly  bodies  through  space  ?  The 
history  of  science  shows  that  great  discoveries  are 
made  by  means  of  imaginative  insight,  but  it  also 
teaches  that  mere  imagination  without  dependence 
upon  known  facts  is  frequently  a  source  of  much  mis- 
chief. Mere  theories  without  facts  are  not  only  empty, 
but  often  stand  in  the  way  of  true  knowledge.  The 
fruitful  exercise  of  the  imagination,  if  we  may  judge 
from  the  way  in  which  great  discoveries  have  been  made, 
always  takes  place  in  closest  connection  with  what  ob- 
servation and  experiment  reveal  regarding  the  nature 
of  phenomena.  If  the  imagination  is  to  have  power  to 
discover  any  truth,  it  must  constantly  '  touch  earth,' 
and  be  guided  in  its  course  by  the  nature  of  facts  which 
are  already  known. 

In  framing  hypotheses,  then,  the  imagination  is 
constantly  prompte'd  by  analogies  with  processes  which 
are  more  or  less  familiar.  The  hypothesis,  then,  is  not 
created  by  the  imagination  'out  of  nothing.'  It  is  rather 
an  extension  or  development  of  a  known  law,  than  an 
absolute  creation. 


§  64.    THE   PROOF  OF   AN   HYPOTHESIS  237 

§  64.  The  Proof  of  an  Hypothesis. — We  have  discussed 
the  way  in  which  hypotheses  are  formed,  but  as  yet  have 
said  nothing  regarding  the  means  of  determining  their 
truth  and  falsity.  But  to  form  hypotheses  is  usually 
easy,  to  verify  them  is  often  exceedingly  difficult.  The 
scientific  worker  constantly  finds  that  theories  which  he 
has  formed  are  without  foundation,  and  must  therefore 
be  discarded.  It  is  not  only  essential  that  a  scientific 
investigator  shall  possess  a  mind  fertile  in  ideas  ;  he 
must  also  love  truth  more  than  any  theory,  no  matter 
how  interesting  or  attractive  it  may  appear.  In  behalf 
of  truth,  every  theory  must  be  subjected  to  the  most 
thorough  and  searching  tests  possible ;  if  it  is  not  borne 
out  by  the  facts,  it  must  be  at  once  discarded.  What 
now  is  the  general  method  of  procedure  in  testing  an 
hypothesis  ?  Two  steps  or  stages  may  be  distinguished 
in  this  process:  (i)  We  assume  that  the  hypothesis  is 
true,  and  proceed  to  show  what  are  the  necessary  results 
which  follow  from  it.  In  doing  so  we  proceed  deduc- 
tively ;  that  is,  assuming  the  truth  of  the  hypothesis, 
we  reason  out  what  consequences  it  must  have.  (2)  The 
conclusions  thus  reached  are  compared  with  the  actual 
facts,  as  given  to  us  directly  in  perception,  or  as  deter- 
mined by  experiment.  If  these  are  found  to  agree,  the 
hypothesis  is  regarded  as  true  ;  if  they  do  not  agree,  it 
must  be  discarded  or  modified. 

This  procedure  may  become  clearer  by  considering 
some  concrete  examples.  If  we  were  to  come  on  the 
campus  some  morning  and  find  that  several  branches 
had  been  broken  from  one  of  the  trees,  we  should 
naturally  try  to  explain  this  circumstance  by  making 


238  THE  USE  OF   HYPOTHESES 

some  hypothesis.  Perhaps  the  first  thing  which  would 
occur  to  us  would  be  that  there  had  been  a  violent  wind- 
storm. The  hypothesis  having  been  made,  the  next  step 
would  be  to  look  around  to  see  if  it  could  be  verified. 
'  If  there  has  been  a  cyclone/  we  might  argue,  '  there 
should  be  other  signs  of  its  presence ;  we  should  find 
broken  twigs  and  blown  leaves  lying  about,  and  all  the 
trees  should  present  a  storm-tossed  appearance.'  If 
observation  showed  that  these  things  were  actually 
present,  we  would  consider  our  hypothesis  so  far  con- 
firmed. But  if  not,  our  first  guess  would  be  disproved, 
and  it  would  be  necessary  to  look  about  for  another 
explanation. 

An  excellent  illustration  of  the  way  in  which  an  hypothesis 
becomes  more  and  more  completely  demonstrated,  is  found  in  the 
history  of  the  experiments  by  which  it  was  proved  that  the  atmos- 
phere has  weight.  Galileo  noticed  that  water  will  rise  in  a  pump  only 
about  33  feet.  He  could  not  find  out,  however,  why  it  was  that  the 
water  should  stop  at  this  point.  After  his  death,  his  friend  and  pupil 
Torricelli  took  up  the  problem,  and  asked  himself  :  Why  does  the 
water  rise  at  all  ?  It  then  occurred  to  him  that  air  must  weigh  some- 
thing, and  that  it  might  be  this  weight  on  the  surface  of  the  water 
which  forced  the  water  up  the  pump  when  there  was  no  air  pressing 
it  down.  Now,  if  this  were  so,  he  reasoned,  the  weight  of  the  air 
ought  to  lift  mercury,  which  is  fourteen  times  heavier  than  water,  to 
one-fourteenth  of  the  height.  So  he  took  some  mercury,  and  filling 
a  tube  about  34  inches  long,  turned  it  upside  down  into  a  basin  of 
mercury  which  was  open,  and  therefore  under  the  pressure  of  the 
atmosphere.  The  mercury  began  to  settle  in  the  tube,  and  finally 
rested  at  a  height  of  30  inches.  Torricelli  had  thus  invented  the 
barometer,  an  instrument  which  would  measure  the  weight  of  the 
atmosphere.  It  was  afterwards  suggested  by  the  famous  French 
writer,  Pascal,  that  at  the  top  of  a  high  mountain,  where  there  is  less 


§  64.     THE   PROOF  OF  AN   HYPOTHESIS  239 

air  pressing  downwards,  the  column  of  mercury  should  fall  consid- 
erably if  the  atmosphere  were  really  what  caused  the  water  and  the 
mercury  to  rise.  When  this  experiment  was  made  by  carrying  the 
barometer  to  the  top  of  a  mountain  called  the  Puy  de  Dome,  the  mer- 
cury fell  nearly  three  inches.  Still  further  confirmation  of  Torri- 
celli's  theory  was  afforded  by  the  discoveries  of  Otto  Guericke  of 
Magdeburg.  In  1650  Guericke  invented  the  air-pump.  The  first  use 
which  he  made  of  his  new  invention  was  to  show  that  the  atmos- 
phere is  pressing  down  upon  us  heavily  and  equally  in  all  directions. 
He  fitted  closely  together  two  metal  hemispheres  and  exhausted  the 
air  between  them  by  means  of  his  pump.  It  was  found  that  the 
pressure  of  the  atmosphere  was  so  great  that  it  took  a  great  force  to 
separate  the  hemispheres.1 

To  establish  a  scientific  theory,  then,  there  are  neces- 
sary not  only  a  ready  imagination,  but  also  patience  and 
perseverance  in  the  careful  deduction  of  the  conse- 
quences of  the  theory,  and  in  the  comparison  of  the 
results  thus  obtained  with  the  actual  facts.  Scientific 
work  also  demands  the  utmost  candor  and  openness  of 
mind  on  the  part  of  those  who  engage  in  it.  One  must 
be  willing  to  abandon  any  theory  as  soon  as  it  is  found 
to  disagree  with  the  facts.  And  this  is  by  no  means  an 
easy  thing  to  do.  When  one  has  a  theory  which  suffices 
for  nearly  all  the  facts,  there  is  always  a  temptation  to 
cling  to  it,  and  to  neglect  or  explain  away  any  trouble- 
some or  contradictory  facts.  There  is  no  doubt  that 
the  scientific  explanations  which  have  become  accepted 
and  established  were  not  the  ideas  which  first  happened 
to  occur  to  the  men  with  whose  names  they  are  associ- 
ated. When  Newton  first  attempted  to  work  out  the 
verification  of  the  gravitation  hypothesis,  he  used  the 

1  Cf.  Buckley,  Short  History  of  Natural  Science,  pp.  114-121. 


240  THE  USE  OF   HYPOTHESES 

most  accurate  measurements  he  could  obtain  regarding 
the  size  of  the  earth.  But  in  calculating  on  this  basis 
the  pull  of  the  earth  on  the  moon,  and  the  consequent 
deflection  of  the  moon  from  the  straight  line,  his  results 
came  out  wrong.  That  is,  the  moon  moved  more  slowly 
than  it  ought  to  do  according  to  his  theory.  The  differ- 
ence was  not  great,  but  Newton  could  not  overlook  this 
lack  of  agreement  with  the  observed  facts.  He  put  the 
whole  matter  aside ;  and  it  was  only  when  he  heard 
sixteen  years  later  that  Picart  had  discovered,  from  new 
and  more  accurate  measurements,  that  the  earth  was 
larger  than  had  been  supposed,  that  he  repeated  his 
calculations,  and  found  his  hypothesis  verified. 

Although  it  very  frequently  turns  out,  both  in  every- 
day matters  and  in  scientific  work,  that  our  hypotheses 
are  disproved,  the  negative  answers  thus  obtained  are 
not  without  value.  For  we  are  often  able  at  once  to 
limit  the  number  of  possible  hypotheses.  In  a  field 
where  we  already  possess  some  systematic  knowledge,  it 
is  often  possible  to  say  :  The  explanation  of  this  group 
of  phenomena  must  be  either  a  or  b  or  c.  If,  then,  one 
is  able  to  show  that  neither  a  nor  b  will  afford  the 
required  explanation,  these  negative  conclusions  will 
lead  directly  to  the  establishment  of  c. 

§  65.  Requirements  of  a  Good  Hypothesis. — Various 
conditions  or  requisites  of  a  good  hypothesis  are  laid 
down  by  writers  on  logic.  The  three  laws  which  are 
most  frequently  stated  are  as  follows:  (i)  That  the 
hypothesis  shall  be  conceivable  and  not  absurd.  (2) 
That  it  shall  be  of  such  a  character  that  deductions 


§  65.     REQUIREMENTS  OF  A  GOOD   HYPOTHESIS     241 

can  be  made  from  it.     (3)  That  it  shall  not  contradict 
any  of  the  known  laws  of  nature. 

It  does  not  seem  to  me  that  the  first  law  is  of  much 
value.  It  is  largely  individual  taste  or  education  which 
leads  us  to  pronounce  certain  theories  '  absurd '  or  '  in- 
conceivable.' Thus,  for  a  long  time,  it  seemed  incon- 
ceivable that  the  earth  should  be  round,  and  should 
revolve  on  its  own  axis ;  and  less  than  a  generation 
ago  the  theory  of  evolution,  as  propounded  by  Darwin, 
seemed  to  many  persons  utterly  '  absurd.'  Nor  can  the 
third  law  always  be  applied  as  a  test  of  an  hypothesis, 
for  many  great  discoveries  seemed,  at  the  time  when 
they  were  announced,  to  contradict  known  laws  of  nat- 
ure. The  difficulty  is  that  no  one  is  able  to  affirm, 
unconditionally,  that  a  law  of  nature  forbids  us  to 
make  this  or  that  hypothesis.  Of  course,  we  feel  that 
a  theory  is  very  probably  false  which  is  at  variance  with 
the  law  of  gravity,  or  with  that  of  the  conservation 
of  energy,  or  any  of  the  laws  which  we  regard  as  es- 
tablished beyond  a  reasonable  doubt.  But,  although 
the  chances  are  always  very  greatly  against  any  theory 
which  runs  counter  to  what  are  regarded  as  well-estab- 
lished laws,  there  is  yet  always  a  possibility  that  it  may 
be  true.  There  is  no  law  of  nature  so  certain  as  to  be 
infallible.  Even  those  laws  which  appear  to  be  beyond 
the  possibility  of  doubt,  may  require  to  be  modified  or 
supplemented.  We  may  find  that,  practically,  it  is  not 
wise  to  trouble  ourselves  with  theories  which  undertake 
to  overthrow  the  law  of  gravitation,  or  to  disprove  other 
fundamental  laws  of  the  physical  world.  But  theo- 
retically, at  least,  there  is  always  a  chance  —  in  cases 
R 


242  THE  USE  OF    HYPOTHESES 

such  as  we  have  been  supposing  the  chance  is  almost 
infinitely  small  —  that  the  new  theory  may  be  right,  and 
the  old  one  wrong.  The  practical  objection  to  admit- 
ting the  claims  of  this  canon  is  the  difficulty  in  apply- 
ing it  fairly.  The  phrase,  'contrary  to  the  laws  of 
nature,'  like  'inconceivable,'  and  'absurd,'  is  likely  to  be 
used  to  condemn  any  theory  with  which  one  disagrees. 
In  this  way,  it  is  evident  that  the  very  point  is  begged 
which  is  really  at  issue. 

Of  these  three  canons,  therefore,  the  second  appears  to 
state  the  only  condition  which  is  essential  to  an  hypothe- 
sis. An  hypothesis,  if  it  is  to  be  of  any  value,  must  be 
capable  of  being  proved  or  refuted.  But,  unless  its 
consequences  can  be  shown  by  way  of  deduction,  it 
is  impossible  to  know  whether  it  agrees,  or  does  not 
agree,  with  the  facts  which  it  is  supposed  to  explain. 
An  hypothesis  from  which  nothing  can  be  deduced, 
then,  is  of  no  value  whatever.  It  always  remains  at 
the  stage  of  mere  possibility,  and  without  any  real 
connection  with  fact.  It  is  a  mere  guess  which  has 
no  significance  whatever,  for  it  is  entirely  incapable 
either  of  proof  or  of  disproof. 

In  general,  it  is  possible  to  deduce  the  consequences  of  a  theory 
only  when  the  principle  employed  is  analogous,  in  mode  of  opera- 
tion, to  something  with  which  we  are  familiar.  Thus,  for  example, 
it  is  because  the  ether  is  conceived  as  resembling  other  material 
bodies  in  important  respects  that  it  can  be  used  as  a  principle  of 
explanation.  It  is  assumed  to  be  elastic  and  capable  of  receiving 
and  transmitting  vibrations,  and  as  spread  out  like  other  material 
bodies  in  space.  In  virtue  of  these  similarities  to  other  material 
substances,  it  is  possible  to  deduce  the  consequences  which  such 
a  substance  as  ether  would  imply,  and  to  compare  them  with  the 


§  65.     REQUIREMENTS   OF  A   GOOD    HYPOTHESIS     243 

actual  facts.  But  if  one  should  make  the  assumption  that  certain 
phenomena  are  due  to  some  agency  totally  unlike  anything  of  which 
we  have  any  experience,  a  disembodied  spirit,  or  ghost,  for  example, 
it  would  be  impossible  either  to  prove  or  to  disprove  the  assertion. 
For  knowing  nothing  whatever  of  the  way  in  which  spirits  act,  one 
could  not  say  whether  the  phenomena  to  be  explained,  table-rap- 
ping, planch ette-writing,  etc.,  were  or  were  not  consistent  with  a 
spirit's  nature  and  habits. 

Another  example  of  a  barren  hypothesis  from  which  no  conclu- 
sions can  be  drawn,  is  afforded  by  the  *  catastrophe '  or  f  convulsion ' 
theory  in  geology,  which  was  first  combatted  by  Lyell,  in  his  Prin- 
ciples of  Geology,  published  in  1830.  "  People  had  so  long  held  the 
belief  that  our  earth  had  only  existed  a  few  thousand  years,  that 
when  geologists  began  to  find  a  great  number  of  strange  plants  and 
animals  buried  in  the  earth^s  crust,  immense  thicknesses  of  rock 
laid  down  by  water,  and  whole  mountain  masses  which  must  have 
been  poured  out  by  volcanoes,  they  could  not  believe  that  this  had 
been  done  gradually,  and  only  in  parts  of  the  world  at  a  time,  as  the 
Nile  and  the  Ganges  are  now  carrying  down  earth  to  the  sea,  and 
Vesuvius,  Etna,  and  Hecla  are  pouring  out  lava  a  few  feet  thick 
every  year.  They  still  imagined  that  in  past  ages  there  must  have 
been  mighty  convulsions  from  time  to  time,  vast  floods  swallowing 
up  plants  and  animals  several  times  since  the  world  was  made,  vio- 
lent earthquakes  and  outbursts  from  volcanoes  shaking  the  whole 
of  Europe,  forcing  up  mountains,  and  breaking  open  valleys.  It 
seemed  to  them  that  in  those  times  when  the  face  of  the  earth  was 
carved  out  into  mountains  and  valleys,  table-lands  and  deserts,  and 
when  the  rocks  were  broken,  tilted  up,  and  bent,  things  must  have 
been  very  different  from  what  they  are  now.  And  so  they  made 
imaginary  pictures  of  how  nature  had  worked,  instead  of  reasoning 
from  what  they  could  see  happening  around  them."  1 

The  convulsions,  or  catastrophes,  which  were  thus  assumed  to  take 
place  were  regarded  as  the  result  of  strange  incalculable  forces 
whose  mode  of  operation  could  never  be  exactly  determined. 

1  Buckley,  Short  History  of  Natural  Science,  pp.  441-442. 


244  THE  USE  OF   HYPOTHESES 

Instead  of  these  mysterious  agencies,  Lyell  assumed  that  causes 
similar  to  those  with  Vhich  we  are  now  acquainted  had  been 
acting  uniformly  for  long  ages.  The  nature  of  the  causes  at  work 
being  known,  it  became  possible  to  calculate  the  nature  of  the  effects, 
and  thus  to  reduce  the  facts  of  geology  to  order  and  system.  As 
we  have  already  shown,  hypotheses  which  are  to  prove  really  service- 
able are  formed  by  extending  some  known  principle  through  analogy 
to  a  new  class  of  facts.  The  assumption  of  mysterious  agencies 
and  principles  whose  mode  of  operation  is  unlike  anything  which  is 
known  to  us,  does  not  aid  in  the  extension  of  knowledge. 

References 

W.  S.  Jevons,  Elementary  Lessons  on  Logic,  Ch.  XXX« 
«     «        «        The  Principles  of  Science,  <3\.  XXIII. 
C.  Sigwart,  Logic,  §  83. 
B.  Bosanquet,  Logic,  Vol.  II.,  pp.  155-167. 


CHAPTER    XIX 

FALLACIES    OF    INDUCTION 

§  66.  The  Source  of  Fallacy.  —  It  is  necessary  at  the 
close  of  our  discussion  of  the  inductive  methods,  to  say 
•something  regarding  the  errors  to  which  we  are  most 
subject  in  this  kind  of  thinking.  We  have  seen  that 
knowledge  is  the  result  of  the  mind's  own  activity,  and 
that  it  grows  in  completeness  through  a  persistent  effort 
to  keep  distinct  things  which  are  different,  and  to  con- 
nect phenomena  which  belong  together.  Truth,  in  other 
words,  is  gained  by  intellectual  activity.  And,  on  the 
other  hand,  we  fall  into  error,  and  are  led  away  by  false 
arguments  as  a  result  of  mental  indolence.  Thinking  is 
hard  work,  and  there  is  always  a  tendency  to  avoid  it.  As 
a  matter  of  fact,  we  all  think  much  less  frequently  than 
we  suppose.  Usually,  we  are  content  to  follow  familiar 
associations,  and  to  repeat  current  phrases,  without  doing 
any  real  intellectual  work.  The  difficulty  is  that  we  can 
get  along  comfortably  without  thinking  for  the  most 
part  —  more  comfortably,  perhaps,  than  when  we  do 
think.  Then,  again,  the  mind  is  less  directly  under  con- 
trol of  the  will  than  the  body.  One  may  force  himself 
to  sit  down  at  his  desk  and  open  a  book ;  but  it  is  more 
difficult  to  compel  oneself  to  think. 

The  only  way  in  which  we  can  be  saved  from  becom- 
ing '  intellectual  dead-beats/  is  by  the  formation  of  good 

245 


246  FALLACIES   OF  INDUCTION 

mental  habits.  It  requires  eternal  vigilance  and  unceas- 
ing strenuousness  to  prevent  our  degeneration  into  mere 
associative  machines.  What  the  logical  doctrine  of  fal- 
lacies can  do  is  to  put  us  on  our  guard  against  this  ten- 
dency. It  enumerates  and  calls  attention  to  some  of 
the  commonest  and  most  dangerous  results  of  slovenly 
thinking,  in  the  hope  that  the  student  may  learn  to 
avoid  these  errors.  Some  of  the  fallacies  of  which  we 
shall  treat  in  this  chapter,  apply  equally  to  deductive 
or  syllogistic  reasoning,  and  have  been  already  treated 
in  Chapter  XI\  We  shall,  however,  enumerate  them 
here  again  for  the  sake  of  completeness.  It  is  conve- 
nient to  discuss  the  various  fallacies  under  the  following 
heads :  — 

(1)  Fallacies  due  to  the  careless  use  of  Language. 

(2)  Errors  of  Observation. 

(3)  Mistakes  in  Reasoning. 

(4)  Fallacies  due  to  Individual  Prepossessions. 

§  67.  Fallacies  due  to  the  Careless  Use  of  Language.  — 
The  careless  and  unreflective  use  of  words  is  a  very  fre- 
quent source  of  error.  Words  are  the  signs  or  symbols 
of  ideas ;  but  the  natural  sluggishness  of  the  mind  leads 
often  to  a  substitution  of  the  word  for  the  idea.  "  Men 
imagine  that  their  reason  governs  words,  whilst,  in  fact, 
words  react  upon  the  understanding ;  and  this  has  ren- 
dered philosophy  and  the  sciences  sophistical  and  inac- 
tive."1 It  is  much  easier  to  deal  with  counters  than 

1  Bacon,  Novum  Organum,  Aph.  LIX. 


§  67.     THE  CARELESS  USE  OF  LANGUAGE  247 

with  realities.  Since  we  must  use  words  to  express  our 
thoughts,  it  is  almost  impossible  to  prevent  them  from 
becoming  our  masters.  The  dangers  from  the  use  of 
words  has  been  well  represented  by  Locke,  from  whom 
I  quote  the  following  passage  :  — 

"  Men  having  been  accustomed  from  their  cradles  to  learn  words 
which  are  easily  got  and  retained,  before  they  knew  or  had  framed 
the  complex  ideas  to  which  they  were  annexed,  or  which  were  to  be 
found  in  the  things  they  were  thought  to  stand  for,  they  usually  con- 
tinue to  do  so  all  their  lives ;  and,  without  taking  the  pains  neces- 
sary to  settle  in  their  minds  determined  ideas,  they  use  their  words 
for  such  unsteady  and  confused  notions  as  they  have,  contenting 
themselves  with  the  same  words  other  people  use,  as  if  their  very 
sound  necessarily  carried  with  it  constantly  the  same  meaning.  .  .  . 
This  inconsistency  in  men's  words  when  they  come  to  reason  con- 
cerning either  their  tenets  or  their  interest,  manifestly  fills  their 
discourse  with  abundance  of  empty,  unintelligible  noise  and  jargon, 
especially  in  moral  matters,  where  the  words,  for  the  most  part, 
standing  for  arbitrary  and  numerous  collections  of  ideas  not  regu- 
larly and  permanently  united  in  nature,  their  bare  sounds  are  often 
only  thought  on,  or  at  least  very  obscure  and  uncertain  notions 
annexed  to  them.  Men  take  the  words  they  find  in  use  among  their 
neighbours ;  and,  that  they  may  not  seem  ignorant  what  they  stand 
for,  use  them  confidently,  without  much  troubling  their  heads  about 
a  certain  fixed  meaning  ;  whereby,  besides  the  ease  of  it,  they  obtain 
this  advantage :  That,  as  in  such  discourses  they  seldom  are  in  the 
right,  so  they  are  as  seldom  to  be  convinced  that  they  are  in  the 
wrong ;  it  being  all  one  to  go  about  to  draw  men  out  of  their  mis- 
takes who  have  no  settled  notions,  as  to  dispossess  a  vagrant  of  his 
habitation  who  has  no  settled  abode."  * 

(i)  In  treating  of  the  misuse  of  words,  we  mention, 
in  the  first  place,  errors  arising  from  the  use  of  a  word 

1  Essay  Concerning  Human  Understanding,  Bk.  III.  Ch.  X. 


248  FALLACIES   OF  INDUCTION 

or  phrase  in  more  than  one  sense.  This  is  usually 
called  the  fallacy  of  Equivocation.  In  some  cases,  the 
equivocation  may  be  mere  wilful  quibbling  on  the  part 
of  the  person  propounding  the  argument,  as  in  the 
following  example  of  Jevons  :  — 

All  criminal  actions  ought  to  be  punished  by  law, 

Prosecutions  for  theft  are  criminal  actions, 

Therefore  prosecutions  for  theft  ought  to  be  punished  by  law. 

Examples  of  this  kind  do  not  mislead  any  one ;  but  in 
some  instances  the  change  of  meaning  in  words  may 
not  be  perceived,  even  by  the  person  who  employs  the 
argument.  For  example,  one  might  reason  :  — 

It  is  right  to  do  good  to  others, 

To  assist  A  in  obtaining  office  is  to  do  him  good, 

Therefore  it  is  right  to  assist  him  in  this  way. 

Here  the  phrase  which  is  used  equivocally  is,  'to  do 
good,'  as  will  at  once  be  perceived. 

(2)  Another  frequent  source  of  error  in  the  use  of 
words  is  found  in  what  has  been  excellently  named 
the  Question-begging  Epithet.  As  is  well  known,  there 
is  much  in  a  name.  Epithets  like  'class-legislation,' 
'compromise  measure,'  '  a  dangerous  and  immoral  doc- 
trine,' are  terms  freely  used  to  describe  the  measures 
or  views  of  opponents.  And,  as  it  is  always  easier  to 
adopt  a  current  phrase,  than  to  examine  the  facts  and 
draw  our  own  conclusions,  it  is  not  surprising  that  the 
name  settles  the  whole  matter  in  the  minds  of  so  many 
people.  Of  course,  the  epithet  employed  may  beg  the 
question  in  favour  of  the  subject  it  is  used  to  describe, 
as  well  as  against  it.  Politicians  well  understand  the 


§  67.    THE  CARELESS   USE  OF  LANGUAGE  249 

importance  of  adopting  an  impressive  and  sonorous  . 
election  cry  to  represent  the  plank  of  their  party.  Thus, 
party  cries  like  *  honest  money,'  '  prohibition  and  prosper- 
ity,' '  the  people's  cause/  etc.,  are  essentially  question- 
begging  epithets.  Even  words  like  'liberty,'  'justice/ 
and  'patriotism/  are  frequently  used  in  such  a  way  as 
to  bring  them  under  the  class  of  fallacies  which  we 
have  here  described.  Under  this  heading,  also,  may  be 
grouped  '  cant '  words  and  phrases.  When  we  accuse 
a  person  of  using  cant,  we  always  imply  that  he  is 
more  or  less  consciously  insincere,  that  he  is  profess- 
ing opinions  and  sentiments  which  he  does  not  really 
possess.  Any  insincere  expression  which  is  made  pri- 
marily for  the  sake  of  effect  may  be  rightly  termed 
cant.  It  is  not  even  necessary  that  the  speaker  should 
be  fully  conscious  of  his  insincerity.  A  man  may  easily 
deceive  himself,  and,  as  he  repeats  familiar  words  and 
phrases,  imagine  himself  to  be  overflowing  with  patriot- 
ism, or  with  sympathy  for  others,  or  with  religious 
feelings. 

(3)  Figurative  language  is  another  frequent  source  of 
error.  Of  the  various  figures  of  speech,  perhaps  meta- 
phors are  the  most  misleading.  The  imagery  aroused 
by  metaphorical  language  is  usually  so  strong  as  to  make 
us  forget  the  difference  between  the  real  subject  under 
consideration,  and  the  matter  which  has  been  used  to 
illustrate  it.  Thus  in  discussing  problems  of  mind,  it 
is  very  common  to  employ  metaphors  drawn  from  the 
physical  sciences.  For  example,  we  read  in  works  on 
psychology  and  ethics  of  '  the  struggle  of  ideas/  of  '  the 
balancing  and  equilibration  of  motives/  of  '  action  in 


250  FALLACIES   OF  INDUCTION 

the  direction  of  the  strongest  motive,'  etc.  Another 
illustration,  which  has  been  often  quoted,  is  Carlyle's 
argument  against  representative  government  founded 
on  the  analogy  between  the  ruler  of  a  state  and  the 
captain  of  a  ship.  The  captain,  he  says,  could  never 
bring  the  ship  to  port  if  it  were  necessary  for  him 
to  call  the  crew  together,  and  get  a  vote  every  time 
he  wished  to  change  the  course.  The  real  differences 
between  the  relation  of  a  captain  to  his  crew,  and  the 
executive  officers  in  a  state  to  the  citizens,  is  lost  sight 
of  by  the  metaphor.  Metaphorical  reasoning  is  simply 
a  case  of  analogy,  the  imperfections  and  dangers  of 
which  have  been  already  pointed  out.  It  is,  however, 
one  of  the  errors  which  it  is  most  difficult  to  avoid.  A 
hidden  metaphor  lurks  unsuspected  in  many  of  the 
words  in  common  use.  We  may  thus  appreciate  the 
force  of  Heine's  humorous  petition :  "  May  Heaven 
deliver  us  from  the  Evil  One,  and  from  metaphors."  l 

§  68.  Errors  of  Observation.  —  Sometimes  insufficient 
observation  is  the  result  of  a  previously  conceived  the- 
ory ;  sometimes  it  may  be  due  to  inattention,  to  the 
difficulties  of  the  case,  or  to  lack  of  the  proper  instru- 
ments and  aids  to  observation.  We  have  already  had 
occasion  to  refer  to  the  influence  of  a  theory  on  obser- 
vation (cf.  §  62).  As  a  rule,  we  see  only  those  instances 
which  are  favourable  to  the  theory  or  belief  which  we 
already  possess.  It  requires  a  special  effort  of  attention 
to  take  account  of  negative  instances,  and  to  discover  the 

1  Quoted  by  Minto,  Logic,  p.  373. 


§68.     ERRORS  OF  OBSERVATION  251 

falsity  involved  in  some  long-standing  belief.  Indeed,  it 
perhaps  requires  quite  as  much  mental  alertness  to  over- 
throw an  old  theory,  as  to  establish  a  new  one.  This 
tendency  of  the  mind  to  seize  upon  affirmative  instances, 
and  to  neglect  the  evidence  afforded  by  negative  cases, 
is  well  set  forth  by  Bacon  in  the  following  passage :  — 

"  The  human  understanding,  when  any  proposition  has  been  once 
laid  down  (either  from  general  admission  and  belief,  or  from  the 
pleasure  it  affords),  forces  everything  else  to  add  fresh  support  and 
confirmation ;  and  although  most  cogent  and  abundant  instances 
may  exist  to  the  contrary,  yet  either  does  not  observe  or  despises 
them,  or  gets  rid  of  and  rejects  them  by  some  distinction,  with 
violent  and  injurious  prejudice,  rather  than  sacrifice  the  authority  of 
its  first  conclusions.  It  was  well  answered  by  him  who  was  shown 
in  a  temple  the  votive  tablets  suspended  by  such  as  had  escaped  the 
peril  of  shipwreck,  and  was  pressed  as  to  whether  he  would  then 
recognize  the  power  of  the  gods ;  '  But  where  are  the  portraits  of 
those  who  have  perished  in  spite  of  their  vows?1  All  superstition  is 
much  the  same,  whether  it  be  that  of  astrology,  dreams,  omens, 
retributive  judgment,  or  the  like,  in  all  of  which  the  deluded  ob- 
servers observe  events  which  are  fulfilled,  but  neglect  and  pass  over 
their  failure,  though  it  be  much  more  common.  But  this  evil  insin- 
uates itself  still  more  craftily  in  philosophy  and  the  sciences,  in 
which  a  settled  maxim  vitiates  and  governs  every  other  circumstance, 
though  the  latter  be  much  more  worthy  of  confidence.  Besides, 
even  in  the  absence  of  that  eagerness  and  want  of  thought  (which 
we  have  mentioned),  it  is  the  peculiar  and  perpetual  error  of  the 
human  understanding  to  be  more  moved  and  excited  by  affirmatives 
than  negatives,  whereas  it  ought  duly  and  regularly  to  be  impartial ; 
nay,  in  establishing  any  true  axiom  the  negative  instance  is  the  most 
powerful."1 

The  nature  of  this  fallacy  has  been  so  well  illustrated 

1  Novum  Organum,  Bk.  I.  Aph.  XLVI. 


252  FALLACIES  OF  INDUCTION 

by  the  quotation  which  has  just  been  given,  that  we  may 
pass  on  at  once  to  speak  of  other  cases  of  insufficient 
observation.  Our  discussion  of  the  processes  of  reason- 
ing have  made  it  clear  how  necessary  it  is  to  observe 
carefully  and  attentively.  The  majority  of  the  false 
theories  which  have  appeared  in  science  and  in  philoso- 
phy, as  well  as  those  of  common  life,  have  arisen  from 
lack  of  observation.  The  doctrine  of  innate  ideas,  and 
the  theory  that  combustion  was  a  process  of  giving  off 
phlogiston  —  a  substance  supposed  to  be  contained  in 
certain  bodies  —  may  be  given  as  examples.  In  some 
seaside  communities,  there  is  a  belief  that  living  beings, 
both  human  and  animal,  never  die  at  flood  tide.  'They 
always  go  out  with  the  ebb,'  it  is  said.  Again,  there  is 
a  general  belief,  which  was  shared  by  such  an  eminent 
scientist  as  Herschel,  that  the  full  'moon  in  rising  pos- 
sesses some  power  of  dispersing  the  clouds.  Careful 
observations  made  at  the  Greenwich  observatory  have, 
however,  shown  conclusively  that  the  moon  has  no  such 
power  as  that  supposed.1 

Another  circumstance  to  be  considered  in  this  con- 
nection is  the  inaccuracy  and  fallibility  of  ordinary 
memory.  Every  one  must  have  noticed  how  rarely  two 
persons  agree  completely  in  the  report  which  they  give 
of  a  conversation  which  they  have  heard,  or  of  events 
which  they  have  experienced.  This  is  due  in  part  to 
diversity  of  interest :  each  person  remembers  those  cir- 
cumstances in  which  for  any  reason  he  is  most  strongly 
interested.  But,  in  addition,  it  is  largely  the  result  of 

1  Cf.  Jevons,  Principles  of  Science,  Ch.  XVIII. 


§  68.     ERRORS   OF  OBSERVATION  253 

the  inevitable  tendency  of  the  mind  to  confuse  what  is 
actually  observed,  with  inferences  made  from  its  obser- 
vations. The  inability  to  distinguish  between  what  is 
really  perceived,  and  what  is  inferred,  is  most  strongly 
marked  in  uneducated  persons,  who  are  not  on  their 
guard  against  this  fallacy.  An  uneducated  person  is  cer- 
tain to  relate,  not  what  he  actually  saw  or  heard,  but  the 
impression  which  the  events  experienced  made  upon 
him.  He  therefore  mixes  up  the  facts  perceived,  with 
his  own  conclusions  drawn  from  them,  and  with  state- 
ments of  his  own  feelings  in  the  circumstances.  A 
lawyer  who  has  to  cross-examine  a  witness  is  usually 
well  aware  of  this  tendency,  and  takes  advantage  of  it 
to  discredit  the  testimony.  The  experienced  physician 
knows  how  worthless  is  the  description  of  symptoms 
given  by  the  ordinary  patient,  or  by  sympathetic  friends, 
or  by  an  inexperienced  nurse.  The  more  one's  sympa- 
thies and  interests  are  aroused  in  such  a  case,  the  more 
difficult  it  is  to  limit  oneself  to  an  exact  statement  of 
actual  occurrences. 

But  this  tendency  is  not  confined  to  persons  deficient 
in  knowledge  and  ordinary  culture.  It  usually  requires 
special  training  to  make  one  a  good  observer  in  any 
particular  field.  It  is  by  no  means  so  easy  as  it  may 
appear  to  describe  exactly  what  one  has  seen  in  an 
experiment.  If  we  know,  or  think  that  we  know, 
the  explanation  of  the  fact,  there  is  an  almost  inevita- 
ble tendency  to  substitute  this  interpretation  for  the 
account  of  what  has  been  actually  observed.  Recent 
psychological  investigation,  aided  by  exact  experimental 
methods,  has  done  much  to  disentangle  the  data  of 


254  FALLACIES  OF  INDUCTION 

perception  from  inferences  regarding  these  data.  As 
every  one  knows  who  has  practised  psychological  intro- 
spection, it  is  only  with  the  utmost  difficulty,  and  after 
long  training,  that  one  can  distinguish  the  actual  psy- 
chological process  present  to  consciousness,  from  the 
associative  and  logical  elements  which  are  bound  up 
with  them  in  our  ordinary  experience.  The  following 
passage  from  Mill  deals  with  this  question  :  — 

"  The  universality  of  the  confusion  between  perceptions  and  the 
inferences  drawn  from  them,  and  the  rarity  of  the  power  to  discrimi- 
nate the  one  from  the  other,  ceases  to  surprise  us  when  we  consider 
that  in  the  far  greater  number  of  instances  the  actual  perceptions  of 
our  senses  are  of  no  importance  or  interest  to  us  except  as  marks 
from  which  we  infer  something  beyond  them.  It  is  not  the  colour 
and  superficial  extension  perceived  by  the  eye  that  are  important  to 
us,  but  the  object  of  which  these  visible  appearances  testify  the 
presence ;  and  where  the  sensation  itself  is  indifferent,  as  it  gener- 
ally is,  we  have  no  motive  to  attend  particularly  to  it,  but  acquire  a 
habit  of  passing  it  over  without  distinct  consciousness,  and  going  on 
at  once  to  the  inference.  So  that  to  know  what  the  sensation  ac- 
tually was  is  a  study  in  itself,  to  which  painters,  for  example,  have 
to  train  themselves  by  long-continued  study  and  application.  In 
things  further  removed  from  the  dominion  of  the  outward  senses, 
no  one  who  has  not  had  great  experience  in  psychological  analysis 
is  competent  to  break  this  intense  association ;  and  when  such  ana- 
lytic habits  do  not  exist  in  the  requisite  degree,  it  is  hardly  possible 
to  mention  any  of  the  habitual  judgments  of  mankind,  from  the 
being  of  God  and  the  immortality  of  the  soul  down  to  the  multi- 
plication table,  which  are  not,  or  have  not  been,  considered  as  mat- 
ter of  direct  intuition." 1 

§  69.  Mistakes  in  Reasoning. — The  problem  of  the 
inductive  processes  of  reasoning  is  to  ascertain  what 

^  Logic,  Bk.  V.  Ch.  IV.  §5. 


§69.     MISTAKES   IN   REASONING  255 

facts  are  necessarily  and  essentially  connected,  and  to 
explain  this  connection.  Now,  in  order  to  distinguish 
between  chance  conjunctions  of  phenomena,  and  real 
causal  connections,  careful  and  extensive  observation, 
aided  whenever  possible  by  experiment,  must  be  em- 
ployed. In  short,  to  establish  a  real  law  of  connection 
between  phenomena,  it  is  necessary  to  use  one  or  more 
of  the  inductive  methods  described  in  Chapters  XIV. 
and  XV.  But  to  do  this  implies,  in  many  cases,  long 
processes  of  analysis;  the  performance  of  intellectual 
work,  which  ordinary  minds,  at  least,  have  the  tendency 
to  shirk  whenever  possible.  It  is  much  easier  to  allow 
associations  to  control  our  thoughts,  and  to  assume  that 
events  which  happen  together  in  our  experience  a  num- 
ber of  times  are  causally  connected.  We  are  led  to 
such  a  conclusion  by  a  natural  psychological  tendency, 
without  taking  any  thought  about  the  matter,  while 
logical  analysis  and  discrimination  require  a  distinct 
conscious  effort. 

The  general  name  used  to  describe  fallacies  which 
are  due  to  this  particular  form  of  mental  sluggishness 
is  post  hoc,  ergo  propter  hoc.  Two  events  occur  in  close 
conjunction  with  each  other,  and  it  is  then  assumed 
without  further  investigation  that  they  are  related  to 
each  other  as  cause  and  effect.  Many  popular  supersti- 
tions, are  examples  of  this  fallacy.  Some  project  begun 
on  Friday  turns  out  disastrously,  and  it  is  inferred  that 
some  causal  relation  existed  between  the  fate  of  the 
enterprise,  and  the  day  on  which  it  was  begun.  Or 
thirteen  persons  sit  down  to  dinner  together,  and  some 
one  dies  before  the  year  is  out.  It  is  to  be  noticed  that 


2$6  FALLACIES  OF  INDUCTION 

such  beliefs  are  supported  by  the  tendency,  to  which 
we  referred  in  the  last  section,  to  observe  only  the 
instances  in  which  the  supposed  effect  follows,  and  to 
neglect  the  negative  cases,  or  cases  of  failure.  '  Fortune 
favours  fools,'  we  exclaim  when  we  hear  of  any  piece 
of  good  luck  happening  to  any  one  not  noted  for  his 
wisdom.  But  we  fail  to  take  account  of  the  more 
usual  fate  of  the  weak-minded.  The  belief  that  the 
full  moon  in  rising  disperses  the  clouds,  which  was  also 
quoted  earlier,  is  a  good  example  of  post  hoc,  propter  hoc. 
In  fact,  all  the  fallacies  treated  in  this  chapter,  except 
those  due  to  language,  might  quite  properly  be  included 
under  this  heading. 

A  special  case  of  this  fallacy,  to  which  attention  may 
be  called  separately,  arises  from  hasty  generalization,  or 
generalization  on  an  insufficient  basis  of  fact.  There 
is  a  constant  tendency  on  the  part  of  the  mind  to  seek 
general  conclusions,  to  express  all  its  knowledge  in  the 
form  of  general  statements.  But,  although  it  is  the 
aim  of  science  to  express  the  truth  regarding  the  nature 
of  the  world  in  the  form  of  general  laws,  it  is  not  allow- 
able to  hurry  on  to  such  principles  without  first  making 
our  observation  of  the  facts  as  complete  as  possible. 
Thus  it  is  not  unusual  to  hear  a  traveller  declare,  on 
the  basis  of  a  very  limited  experience,  that  '  the  hotels 
of  some  city  or  country  are  thoroughly  bad.'  The 
generalizations  which  are  so  frequently  made  regarding 
the  peculiar  characteristics  of  Americans,  or  English- 
men, or  Frenchmen  are  usually  of  the  same  sort.  Con- 
clusions regarding  the  effect  of  moral  and  political 
conditions,  too,  are  often  drawn  from  observations  in 


§70.  FALLACIES  DUE  TO  INDIVIDUAL  PREPOSSESSIONS    257 

a  limited  field.  Even  scientific  books  are  not  always 
free  from  this  error.  In  a  recently  published  psycho- 
logical study  of  the  first  year  of  the  life  of  a  child, 
by  the  mother,  it  was  explained  why  a  baby  always 
sucks  its  thumb  rather  than  its  fingers.  The  explana- 
tion was  that  the  thumb,  being  on  the  outside  and  pro- 
jecting outwards,  got  oftenest  into  the  baby's  mouth, 
and  so  the  habit  was  formed.  The  point  is,  that  the 
mother  assumed  what  she  had  observed  in  her  own 
child  to  be  true  universally.  Other  parents,  however, 
declare  that  their  babies  never  put  the  thumb  into  the 
mouth,  but  always  the  fingers  or  the  whole  hand. 

§  70.  Fallacies  due  to  Individual  Prepossessions.  — 
Bacon  named  this  class  of  fallacy  "The  Idols  of  the 
Cave."  Each  individual,  as  he  represents  the  matter, 
is  shut  up  in  his  own  cave  or  den  ;  that  is,  he  judges 
of  things  from  his  own  individual  point  of  view.  In 
the  first  place,  one's  inclinations  and  passions,  likes 
and  dislikes,  pervert  one's  judgment.  It  is  exceed- 
ingly difficult,  as  we  all  know,  to  be  fair  to  a  person 
we  dislike,  or  to  refrain  from  judging  too  leniently 
the  shortcomings  of  those  to  whom  we  are  warmly 
attached.  Again,  it  is  not  easy  to  put  oneself  in 
the  position  of  an  impartial  spectator  when  one's 
interests  are  at  stake.  "  The  understanding  of  men," 
says  Bacon,  "  resembles  not  a  dry  light,  but  admits 
some  tincture  of  the  passions  and  will."  Further- 
more, each  individual  has  a  certain  personal  bias  as  a 
result  of  his  natural  disposition  and  previous  training. 
Thus  it  is  almost  impossible  for  an  individual  to  free 


258  FALLACIES  OF  INDUCTION 

himself  from  national  prejudices,  or  from  the  standpoint 
of  the  political  party,  or  the  church  in  which  he  was 
brought  up.  Or,  if  a  person  does  give  up  his  old  views, 
he  not  infrequently  is  carried  to  the  opposite  extreme, 
and  can  see  no  good  in  what  he  formerly  believed. 
Even  education  and  the  pursuit  of  special  lines  of 
investigation  may  beget  prejudices  in  favour  of  particular 
subjects.  When  a  man  has  been  engaged  exclusively  for 
a  long  time  in  a  particular  field,  employing  a  particular 
set  of  conceptions,  it  is  almost  inevitable  that  he  should 
look  at  everything  with  which  he  has  to  do  in  the  same 
light.  The  mathematician's  view  of  the  world  is  almost 
sure  to  be  different  from  that  of  the  historian,  or  that 
of  the  student  of  aesthetics.  It  is  very  difficult  for  the 
physicist  to  conceive  of  any  natural  process  except  in 
terms  of  molecules  and  vibrations.  It  is  inevitable  that 
each  man  should  be  blinded  to  some  extent  by  his  own 
presuppositions.  But  to  recognize  one's  limitations  in 
this  respect,  is  to  pass,  to  some  extent  at  least,  beyond 
them. 

Moreover,  each  age,  as  well  as  each  individual,  may  be  regarded 
as  governed  largely  by  current  presuppositions  and  prejudices. 
Throughout  the  Middle  Ages,  theological  doctrines  and  opinions 
controlled  almost  absolutely  the  opinions  and  beliefs  of  mankind. 
This  influence,  doubtless,  still  makes  itself  felt,  but  people  are  now 
pretty  generally  awake  to  the  dangers  from  this  source.  On  the 
other  hand,  it  is  more  difficult  to  realize  at  the  present  time  that 
it  is  not  impossible  for  prejudices  and  prepossessions  to  grow  out 
of  scientific  work.  The  success  of  modern  scientific  methods 
has  sometimes  led  investigators  to  despise  and  belittle  the  work  of 
those  who  do  not  carry  on  their  investigations  in  laboratories,  or  do 
not  weigh  and  measure  everything.  But  conceptions  and  methods 


§70.  FALLACIES  DUE  TO  INDIVIDUAL  PREPOSSESSIONS    259 

which  prove  useful  in  one  science  cannot  always  be  employed  profit- 
ably in  another.  A  conception,  or  mode  of  regarding  things,  which 
has  proved  serviceable  in  one  field  is  almost  certain  to  dominate  a 
whole  age,  and  to  be  used  as  an  almost  universal  principle  of  ex- 
planation. The  eighteenth  century,  for  example,  was  greatly  under 
the  influence  of  mechanical  ideas.  Newton's  discovery  made  it  pos- 
sible to  regard  the  world  as  a  great  machine,  the  parts  of  which 
were  all  fitted  together  according  to  the  laws  of  mechanics.  This 
view  led  to  such  a  vast  extension  of  knowledge  in  the  realm  of 
physics  and  astronomy,  that  the  conceptions  upon  which  it  is  based 
were  applied  in  every  possible  field  —  to  psychology,  to  ethics,  to 
political  science.  The  world  itself,  as  well  as  religious  creeds  and 
political  and  social  institutions,  were  supposed  to  have  been  de- 
liberately made  and  fashioned  by  some  agent.  Again,,  in  these  later 
years  of  the  nineteenth  century  we  are  dominated  by  the  idea  of 
evolution.  The  biological  notion  of  an  organism  which  grows  or 
develops  has  been  applied  in  every  possible  field.  We  speak,  for 
example,  of  the  world  as  an  organism  rather  than  as  a  machine,  of  the 
state  and  of  society  as  organic.  And  the  same  conception  has  been 
found  useful  in  explaining  the  nature  of  human  intelligence.  It  is 
easy  for  us  to  realize  the  limitations  and  insufficiency  of  the  notion 
of  mechanism  as  employed  by  the  thinkers  of  the  eighteenth  century. 
But  it  is  not  improbable  that  the  twentieth  century  may  be  able  to 
see  more  clearly  than  we  are  able  to  do,  the  weaknesses  and  limita- 
tions of  the  conception  which  has  proved  so  fruitful  in  this  genera- 
tion. 

References 

Bacon,  Novum  Organum,  Aph.  XXXVIII-LXVIII. 
Locke,  Essay  Concerning  Human  Understanding,  Bk.  III.  Chs. 
X.  and  XI. 

J.  S.  Mill,  Logic,  Book  V. 

A.  Bain,  Logic,  Pt.  II.  Induction,  Bk.  VI. 

J.  Fowler,  Inductive  Logic,  Ch.  VI. 

J.  G.  Hibben,  Inductive  Logic,  Ch.  XVII. 

A.  Sidgwick,  Fallacies  [Int.  Scient.  Series]. 


PART    III.  — THE    NATURE    OF 
THOUGHT 

CHAPTER  XX 

JUDGMENT    AS    THE    ELEMENTARY    PROCESS    OF    THOUGHT 

§  71.  Thinking  the  Process  by  which  Knowledge  grows 
or  develops.  —  Logic  was  defined  (§  i)  as  the  science  of 
thinking,  and  we  have  seen  that  the  business  of  thought 
is  to  furnish  the  mind  with  truth  or  knowledge.  Under 
what  general  conception,  now,  shall  we  bring  thinking, 
and  what  method  shall  we  adopt  to  aid  us  in  its  investi- 
gation ?  It  is  at  once  clear  that  thinking,  the  conscious 
process  by  which  knowledge  is  built  up,  does  not  re- 
semble mechanical  processes  like  pressure,  or  attraction 
and  repulsion.  It  is  more  nearly  related  to  something 
which  has  life,  like  a  plant  or  an  animal,  and  which 
grows  or  develops  from  within,  in  accordance  with  the 
laws  of  its  own  nature.  Thinking  must  be  regarded 
rather  as  a  living,  than  as  a  dead  thing,  though  it  is 
necessary  also  to  remember  that  it  is  conscious  as  well 
as  living. 

When  the  thinking  process  is  regarded  in  this  way, 
moreover,  a  method  of  procedure  at  once  suggests  itself. 
In  these  days  we  have  become  familiar  with  the  notion 
of  evolution  or  development,  and  the  application  of  this 

260 


§  7i.    THE  PROCESS   OF  THINKING  26 1 

notion  has  proved  of  the  greatest  service  to  science,  and 
particularly  to  those  sciences  which  deal  with  the  phe- 
nomena of  life.  What  is  characteristic  of  this  manner  of 
regarding  things  is  the  fact  that  it  does  not  consider  the 
various  phenomena  with  which  it  deals  as  fixed,  un- 
changeable things,  each  with  a  ready-made  nature  of  its 
own.  But  each  thing  is  simply  a  stage  of  a  process,  a 
step  on  the  way  to  something  else.  And  the  relations 
of  the  various  phenomena  to  each  other,  their  connec- 
tion and  unity  as  parts  of  the  one  process,  come  out 
more  clearly  when  viewed  in  this  way.  In  other  words, 
by  taking  a  survey  of  the  genesis  and  growth  of  things, 
we  gain  a  truer  idea  of  their  nature  and  relations  than 
would  be  possible  in  any  other  way.  The  past  history 
of  any  phenomenon,  the  story  of  how  it  came  to  be 
what  it  is,  is  of  the  greatest  possible  service  in  throwing 
light  upon  its  real  nature.  Now,  one  cannot  doubt 
that  this  conception  will  also  prove  serviceable  in  the 
study  of  logic.  That  is  to  say,  it  will  assist  us  in  .gain- 
ing a  clearer  idea  of  the  nature  of  thinking,  to  conceive 
it  as  a  conscious  function,  or  mode  of  acting,  which  un- 
folds or  develops  in  accordance  with  the  general  laws  of 
organic  evolution.  And  this  process  may  be  supposed 
to  go  on  both  in  the  individual,  as  his  thought  develops 
and  his  knowledge  expands,  and  in  the  race,  as  shown 
by  its  history.  By  adopting  this  notion,  we  may  hope 
to  show  also  that  there  is  no  fundamental  difference 
in  kind  between  the  various  intellectual  operations. 
Judgment  and  Inference,  for  example,  will  appear  as 
stages  in  the  one  intellectual  process,  and  the  relation 
between  Induction  and  Deduction  will  become  evident. 


262.        JUDGMENT  AS  THE  ELEMENTARY   PROCESS 

§  72.   The  Law  of  Evolution  and  its  Application  to  Logic. 

—  The  most  striking  characteristic  of  any  organism  at  a 
low  stage  of  development  is  its  almost  complete  lack  of 
structure.  An  amoeba,  for  example,  can  scarcely  be 
said  to  have  any  structure  ;  it  is  composed  of  protoplasm 
which  is  almost  homogeneous,  or  of  the  same  character 
throughout.  When  we  compare  an  amoeba,  however, 
with  an  animal  much  higher  in  the  scale  of  life,  e.g., 
a  vertebrate,  a  great  difference  is  at  once  evident. 
Instead  of  the  simple,  homogeneous  protoplasm,  the 
organism  is  composed  of  parts  which  are  unlike  or  hete- 
rogeneous, such  as  bones,  muscles,  tendons,  nerves, 
blood-vessels,  etc.  In  Mr.  Spencer's  language,  there 
has  been  a  change  from  a  state  of  homogeneity,  to 
one  of  heterogeneity.  The  process  of  evolution  from 
the  lower  organism  to  the  higher  has  brought  with 
it  a  differentiation  of  structure.  That  is,  in  the  amoeba 
there  are  no  special  organs  of  sight,  or  hearing,  or 
digestion,  but  all  of  these  acts  seem  to  be  performed 
by  any  part  of  the  organism  indifferently.  In  the 
vertebrate,  on  the  other  hand,  there  is  division  of 
labour,  and  a  separate  organ  for  each  of  these  func- 
tions. One  may  also  notice  that  the  same  change  is 
observable  when  the  acts  or  functions,  performed  by  a 
lower  organism  are  compared  with  those  of  a  higher. 
The  life  of  the  amoeba  seems  to  be  limited  almost  en- 
tirely to  assimilation  and  reproduction ;  while,  when  we 
advance  from  the  lower  animals  to  the  higher,  and  from 
the  higher  animals  to  man,  there  is  an  ever-increas- 
ing complexity  and  diversity  in  the  character  of 
the  actions  performed.  We  thus  see  how  the  process 


§  72.     THE  LAW  OF  EVOLUTION  263 

of  evolution  involves  differentiation  both  of  structure 
and  of  function,  in  passing  from  the  homogeneous 
to  the  heterogeneous. 

But  differentiation,  or  increase  in  diversity,  is  only 
one  side  of  the  process  of  evolution.  As  we  pass  from 
a  lower  to  a  higher  stage,  the  various  parts  of  an  or- 
ganism are  seen  to  become  more  essential  to  each  other. 
If  certain  plants  or  low  animal  organisms  are  divided 
into  several  parts,  each  part  will  go  on  living.  Its  con- 
nection with  the  other  parts  does  not  seem  to  have  been 
at  all  necessary  to  it.  But  when  we  are  dealing  with 
higher  forms  of  life,  each  part  is  seen  to  have  its  own 
particular  function,  and  to  be  essential  to  the  other 
parts,  and  to  the  organism  as  a  whole.  In  other  words, 
the  parts  now  become  members,  and  the  whole  is  not 
simply  an  aggregation  of  parts  or  pieces,  but  is  consti- 
tuted by  the  necessary  relation  of  the  members  to  each 
other.  The  more  highly  evolved  the  whole  with  which 
we  are  dealing,  the  more  closely  connected  and  essential 
to  each  other  are  the  various  parts  seen  to  be.  It  be- 
comes increasingly  true  that  if  one  member  suffers,  all 
the  other  members  suffer  along  with  it. 

Evolution,  then,  not  only  exhibits  a  constant  process 
of  differentiation,  and  a  constant  increase  in  the  diver- 
sity of  parts  and  organs,  but  there  goes  along  with  this 
what  might  be  called  a  process  of  unification,  whereby 
the  parts  are  brought  into  ever  closer  and  more  essen- 
tial relation  to  one  another.  In  this  way,  a  real  or  or- 
ganic whole,  as  opposed  to  a  mere  aggregate,  is  formed. 
This  is  what  Mr.  Spencer  calls  the  process  of  integra- 
tion; and  it  accompanies,  as  we  have  seen,  what  the 
same  writer  calls  differentiation. 


264        JUDGMENT  AS  THE  ELEMENTARY  PROCESS 

The  application  of  this  general  law  of  evolution  to 
the  development  of  the  thinking  process  is  not  diffi- 
cult. We  shall  expect  to  find  that  thinking,  in  its 
first  beginnings,  both  in  the  individual  and  in  the  race, 
will  be  much  less  complex  than  at  a  higher  stage. 
That  is,  the  earliest  or  simplest  thinking  tends  to  take 
things  in  a  lump,  without  making  any  distinctions. 
The  infant,  for  example,  does  not  distinguish  one 
person  from  another,  or  perhaps  does  not  distinguish 
even  the  parts  of  its  own  body  from  surrounding  ob- 
jects. Now,  it  is  clear  that  intellectual  development, 
growth  in  knowledge,  must  in  the  first  place  involve 
differentiation.  What  is  complex  must  be  analyzed  or 
separated  into  its  various  parts.  Things  which  are 
different  must  be  distinguished,  and  clearly  marked 
off  from  each  other.  The  development  of  thought 
implies  then,  as  one  of  its  moments,  discrimina- 
tion or  analysis  —  what  we  previously  called  differen- 
tiation. 

The  other  moment  of  the  law  of  evolution,  integration, 
also  finds  a  place  in  the  development  of  thought,  and 
goes  hand  in  hand  with  the  former.  The  child  and  the 
uneducated  man  not  only  often  fail  to  make  distinctions 
where  these  really  exist,  but  the  parts  of  their  know- 
ledge are  fragmentary,  and  have  little  or  no  relation  to 
one  another.  The  various  pieces  of  their  knowledge 
are  like  the  parts  of  the  amoeba  —  they  may  be  in- 
creased or  diminished  without  themselves  undergoing 
any  change.  But  in  order  to  pass  from  a  lower  to  a 
higher  intellectual  point  of  view,  —  to  become  better 
educated,  in  a  word, — it  is  necessary  to  see  the  way  in 


§  72.     THE  LAW   OF  EVOLUTION  265 

which  the  various  pieces  of  our  knowledge  are  con- 
nected and  depend  upon  one  another.  It  is  not  enough 
to  analyze  and  keep  separate  things  which  are  distinct, 
but  it  is  also  necessary  to  understand  how  the  various 
parts  of  our  knowledge  are  so  related  as  to  be  essential 
to  one  another.  In  other  words,  we  may  say  that  it  is 
characteristic  of  our  intelligence  to  endeavour  to  put 
things  together  so  as  to  form  a  whole,  or  system  of 
interconnected  ]5arts.  And  the  more  completely  it  is 
able  to  do  this  (provided  that  the  process  of  differentia- 
tion has  also  made  a  corresponding  advance),  the  higher 
is  the  stage  of  development  which  has  been  attained. 
The  ideal  of  knowledge,  or  of  complete  intellectual 
development,  would  be  to  understand  the  oneness  and 
relation  of  everything  which  exists,  even  of  all  those 
things  which  seem  now  to  be  entirely  different  in  kind. 
A  knowledge  of  any  one  fact  would  then  carry  with  it  a 
knowledge  of  every  other  fact.  Or,  rather,  our  know- 
ledge would  be  so  completely  unified,  that  each  part 
would  show  the  nature  of  the  whole  or  system  to 
which  it  belongs ;  just  as  a  leaf  of  a  plant,  or  the  tooth 
of  an  animal,  is  sufficient  to  tell  the  naturalist  of  the 
wholes  to  which  they  belong. 

This,  of  course,  will  always  remain  an  ideal ;  but  it  is 
in  this  direction  that  thinking  actually  develops.  It  is 
a  step  in  advance  to  discover  the  reasons  for  any  fact 
which  one  previously  knew  as  a  mere  fact.  But,  to 
discover  the  reasons  for  a  fact,  is  to  bring  it  into  con- 
nection with  other  facts,  to  see  them  no  longer  as 
isolated  and  independent,  but  as  belonging  together 
to  one  group  or  system  of  facts.  And  the  further 


266        JUDGMENT  AS  THE   ELEMENTARY  PROCESS 

the  process  of  explanation  goes  on,  the  more  completely 
is  our  knowledge  unified  and  related. 

There  is,  however,  another  fact  implied  in  the  very 
nature  of  evolution,  of  which  logic,  as  well  as  the  other 
sciences,  may  take  advantage.  We  have  assumed  that 
the  more  complete  and  difficult  kinds  of  thinking  have 
grown  or  developed  from  simpler  types  of  the  same 
process,  and  not  from  something  different  in  kind.  It 
will  therefore  follow,  that  the  essential  characteristics  of 
the  thinking  process  may  be  discovered  in  its  simplest 
and  most  elementary  form.  It  is  found  that  all  the 
essential  functions  of  the  fully  developed  organism  are 
discharged  by  the  primitive  cell.  And  because  it  is 
easier  to  study  what  is  simple  than  what  is  complex, 
the  cell  is  taken  as  the  starting-point  in  biology.  Simi- 
larly, there  will  be  an  advantage  in  beginning  with  the 
simplest  and  most  elementary  forms  of  thinking.  What 
is  found  true  of  these  simple  types  of  thought,  may  be 
assumed  to  be  essential  to  the  thinking  process  as  such. 

§  73.  Judgment  as  the  Starting-point.  —  What,  then, 
is  the  simplest  form  of  thinking  ?  What  shall  we  take 
as  a  starting-point,  which  will  correspond  to  the  cell  in 
biology,  or  the  elementary  process  in  psychology  ?  To 
answer  this  question,  it  is  not  necessary  first  to  decide 
where  in  the  scale  of  animal  life  that  which  we  are  en- 
titled to  call  thinking  actually  begins.  We  shall  not  be 
obliged  to  discuss  the  much-debated  question,  whether 
or  not  dogs  think.  Wherever  thinking  may  be  found, 
it  is  essentially  an  activity  of  the  mind.  When  it  is 
present,  that  is,  there  is  always  work  done,  something 


§  73-    JUDGMENT  AS  THE  STARTING-POINT         267 

interpreted  or  put  together,  and  a  conclusion  reached. 
One  may  perhaps  say  that  thinking  is  simply  the  way 
in  which  the  mind  puts  two  and  two  together  and  sees 
what  the  result  is.  It  implies  that  the  mind  has  waked 
up  to  the  significance  of  things,  and  has  interpreted 
them  for  itself.  Suppose  that  one  were  sitting  in  one's 
room  very  much  engaged  with  some  study,  or  wrapt  up 
in  an  interesting  book,  and  suppose  that  at  the  same 
time  the  sound  of  a  drum  fell  upon  one's  ears.  Now, 
the  sound  sensations  might  be  present  to  consciousness 
without  calling  forth  any  reaction  on  the  part  of  the 
mind.  That  is,  we  might  be  so  intent  on  our  book  that 
we  should  not  wake  up,  as  we  have  been  saying,  to  the 
meaning  or  significance  of  the  drum-taps ;  or  perhaps 
not  even  to  the  fact  that  they  were  drum-taps  at  all. 
But  if  the  mind  did  react  upon  the  sound  sensations, 
it  would  try  to  interpret  them,  or  put  them  together  so 
as  to  give  them  a  meaning.  As  a  result,  some  conclu- 
sion would  be  reached,  as,  for  example,  'the  drum  is 
beating ' ;  or  sufficient  intellectual  work  may  have  been 
done  to  give  as  a  conclusion,  '  that  is  the  Salvation  Army 
marching  up  the  street.'  In  any  case,  it  is  of  the  great- 
est importance  to  notice  that  the  conclusion  does  not 
come  into  our  minds  from  without,  but  that  it  is  the 
product  of  the  mind's  own  activity,  as  has  been  de- 
scribed. It  is  not  true,  in  other  words,  that  knowledge 
passes  into  our  minds  through  the  senses ;  it  is  only 
when  the  mind  wakes  up  to  the  meaning  of  sensations, 
and  is  able  to  put  them  together  and  interpret  them, 
that  it  gains  any  knowledge. 

Now,  the  simplest  form  of  such  an  act  of  thought  is 


268         JUDGMENT  AS  THE  ELEMENTARY   PROCESS 

called  a  judgment.  Judgment,  we  may  say,  is  a  single 
intellectual  act  of  the  kind  we  have  described ;  and  its 
conclusion  is  expressed  by  means  of  a  Proposition  ;  as, 
for  example,  'the  grass  is  green/  'the  band  is  playing.' 
In  accordance  with  general  usage,  however,  we  may  use 
the  term  '  Judgment '  for  both  the  act  itself  and  its 
result.  And  the  word  '  Proposition  '  will  then  denote 
the  external  expression  in  speech  or  writing  of  the 
product  of  an  act  of  judgment. 

In  our  investigation  of  the  nature  of  thought,  then, 
we  must  begin  with  Judgment.  There  are  three  things 
which  we  shall  have  to  do  :  (i)  to  endeavour  to  discover 
the  fundamental  characteristics  of  this  simple  type  of 
thinking;  (2)  to  show  the  various  forms  which  it  as- 
sumes, or  to  describe  the  different  kinds  of  Judgment ; 
and  (3)  to  trace  the  process  by  which  Judgment  ex- 
pands into  the  more  complete  logical  form  of  Inference. 
Before  any  of  these  questions  are  considered,  however, 
it  is  necessary  to  meet  a  very  serious  objection  to  our 
whole  procedure  of  beginning  with  Judgment  as  the 
elementary  process  of  thinking. 

§  74.  Concepts  and  Judgments.  —  In  the  last  section, 
we  endeavoured  to  show  that  Judgment  is  the  elemen- 
tary process  of  thought,  and  that  with  it  all  knowledge 
begins.  This  view,  however,  may  seem  to  be  contra- 
dicted by  the  treatment  of  Judgment  usually  found  in 
logical  text-books.  Judgment,  it  is  said,  is  expressed 
by  a  proposition ;  and  a  proposition  is  made  up  of  three 
parts,  subject,  predicate,  and  copula.  Thus  in  the  prop- 
osition, 'iron  is  a  metal/  'iron '  is  the  subject,  'a  metal' 


§  74-     CONCEPTS  AND   JUDGMENTS  269 

the  predicate,  and  the  two  terms  are  joined  or  united  by 
means  of  the  copula  'is.'  A  Judgment  is  therefore 
defined  as  an  act  of  joining  together,  or,  in  negative 
judgments,  of  separating,  two  concepts  or  ideas.  If 
this  account  be  accepted,  it  follows  that  the  ideas  of 
which  the  judgment  is  composed  (iron  and  metal,  in 
the  example  given  above)  are  pieces  of  knowledge 
which  precede  the  judgment  itself.  And  the  act  by 
which  these  logical  ideas  (or,  as  they  are  usually  called, 
concepts)  are  formed  must  also  be  earlier  and  more 
fundamental  than  the  act  of  judging.  It  is  therefore 
held  that  logic  should  begin  with  concepts,  which  are 
the  elements  out  of  which  judgments  are  compounded, 
and  that  the  first  logical  act  consists  in  the  conception 
or  simple  apprehension  of  the  ideas  or  concepts  (cf.  §  1 1). 

It  is  necessary  to  examine  this  position  very  care- 
fully. What  is  maintained  is  that  a  process  of  forming 
concepts,  or  logical  ideas,  presumably  quite  distinct 
from  the  activity  of  judgment,  necessarily  precedes  the 
latter.  Before  it  is  possible  to  judge  that  'iron  is  a 
metal,'  for  instance,  one  must  have  gained,  by  means  of 
Conception  or  Apprehension,  the  ideas  denoted  by  the 
subject  and  predicate  of  this  proposition.  Judgments, 
that  is,  are  made  or  compounded  out  of  something 
different  from  themselves. 

It  may  be  well  to  begin  the  defence  of  our  own 
position  by  noting  what  is  undoubtedly  true  in  what 
has  just  been  stated.  In  making  a  judgment  like  'iron 
is  a  metal,'  it  is,  of  course,  necessary  to  have  the  con- 
cept 'iron,'  and  the  concept  'metal.'  But  what  is 
implied  in  having  a  concept  of  anything?  Let  us 


27O        JUDGMENT   AS  THE   ELEMENTARY   PROCESS 

suppose  that  a  person  is  making  the  above-mentioned 
judgment  for  the  first  time  —  that  is,  really  drawing  a 
conclusion  for  himself,  and  not  merely  repeating  words. 
He  would  begin,  we  may  say,  with  the  concept  'iron.' 
But  if  this  concept  is  more  than  a  mere  word,  if  it 
really  means  anything,  it  must  have  been  formed  by  a 
number  of  judgments.  The  concept  'iron/  if  it  has 
any  significance  for  the  person  using  it,  means  a  defi- 
nite way  of  judging  about  some  substance  —  that  it  is 
hard,  malleable,  tough,  etc.  The  greater  the  number 
of  judgments  which  the  concept  represents,  the  more 
meaning  or  significance  it  has;  apart  from  the  judg- 
ment, it  is  a  mere  word,  and  not  a  thought  at  all. 

To  admit,  then,  that  in  judging  we  always  start  from 
some  concept,  does  not  imply  that  there  is  a  different 
form  of  intellectual  activity  prior  to  judgment,  which 
furnishes  the  latter  with  ready-made  material  for  its 
use.  But,  as  we  have  seen,  in  ordinary  judgments  like 
the  example  with  which  we  have  been  dealing,  the  new 
judgment  is  a  further  expansion  or  development  of  a 
previous  set  of  judgments  which  are  represented  by  the 
concept.  The  concept,  then,  stands  for  the  series  of 
judgments  which  have  already  been  made.  Language 
comes  to  the  aid  of  thought,  and  makes  it  possible  to 
gather  up  such  a  set  of  judgments  and  represent  them 
by  a  single  expression  —  often  by  a  single  word.  Every 
word  that  is  the  name  of  some  logical  concept  repre- 
sents intellectual  work  —  the  activity  of  judgment  —  in 
its  formation.  In  learning  our  own  language,  we 
inherit  the  word  without  doing  the  work.  But  it  must 
never  be  forgotten  that  the  word  in  itself  is  not  the 


§  74-     CONCEPTS  AND  JUDGMENTS  2/1 

concept.  To  make  the  thought  our  own,  to  gain  the 
real  concept,  it  is  necessary  to  draw  out  or  realize  to 
ourselves  the  actual  set  of  judgments  for  which  the 
word  is  but  the  shorthand  expression. 

The  view  which  regards  the  judgment  as  a  compound 
of  two  parts  —  subject  and  predicate  —  rests  upon  the 
substitution  of  words  for  thoughts.  It  analyzes  the 
proposition  (the  verbal  or  written  expression  of 
the  judgment),  instead  of  the  judgment  itself.  In 
the  proposition,  the  parts  do  exist  independently  of 
each  other.  The  subject  usually  stands  first,  and  is 
followed  by  the  predicate.  But  there  is  no  such  order 
of  parts  in  a  judgment.  When  one  judges,  'it  is  rain- 
ing,' or,  '  that  is  a  drum/  the  piece  of  knowledge  is  one 
and  indivisible.  And  the  act  by  which  this  knowledge 
is  gained,  is  not  an  external  process  of  joining  one  part 
to  another,  but  is  an  intellectual  reaction  by  which  we 
recognize  that  something,  not  previously  understood, 
has  a  certain  meaning  or  significance. 

Again,  it  is  only  when  concepts  are  identified  with 
the  words  which  make  up  the  parts  of  the  proposition, 
that  they  can  be  regarded  as  ready-made  existences, 
which  are  quite  independent  of  their  connection  in  a 
judgment.  The  terms,  'iron/  and  'metal/  are  separable 
parts  of  the  proposition  and  exist  independently  of  their 
connection  with  it.  The  conclusion  has  been  therefore 
drawn  that  concepts  had  a  like  independence  of  judg- 
ments, but  might  enter  into  the  latter  and  form  a  part 
of  them  without  affecting  their  own  nature  in  any  way. 
But,  as  we  have  already  seen,  the  concept  has  no 
meaning  apart  from  the  series  of  judgments  which  it 


2/2        JUDGMENT  AS  THE   ELEMENTARY   PROCESS 

represents.  And,  as  thinking  goes  on,  as  new  judg- 
ments are  made,  its  nature  is  constantly  changing.  In 
short,  concepts  are  not  dead  things,  but  living  thoughts 
which  are  in  constant  process  of  development. 

The  objection,  then,  which  urges  that  conception  is  a 
logical  process,  which  is  prior  to  judgment,  turns  out 
when  rightly  understood  to  be  no  objection  at  all.  For, 
in  the  light  of  what  has  been  already  said,  it  only 
amounts  to  this  :  In  making  new  judgments  regarding 
anything,  we  must  set  out  from  what  we  already  know 
of  it,  as  represented  by  the  judgments  already  made. 
That  is,  the  starting-point  for  a  new  judgment  is  the  con- 
cept or  series  of  judgments  which  represents  the  present 
state  of  our  knowledge.  The  progress  of  knowledge 
is  not  from  the  unknown  to  the  known,  but  from  a  state 
of  partial  and  incomplete  knowledge  to  one  of  greater 
perfection.  Thus  the  judgment  'gold  is  malleable' 
(supposing  it  to  be  a  real  judgment  made  for  the  first 
time),  adds  to,  or  develops  further,  our  existing  know- 
ledge of  gold,  as  represented  by  a  series  of  judgments 
previously  made  regarding  it. 

It  may  be  urged,  however,  that  not  every  judgment  can  grow  out 
of  previous  judgments  in  this  way.  For,  if  we  go  back  far  enough, 
we  must  reach  some  judgment  which  is  absolutely  first,  and  which 
presupposes  no  antecedent  judgment.  This  is  like  the  paradox 
regarding  the  origin  of  life.  If  all  judgments  are  derived  from  an- 
tecedent judgments,  how  was  it  possible  for  the  first  one  to  arise? 
It  will,  perhaps,  be  sufficient  answer  to  deny  the  existence  of  the 
paradox.  Consciousness  must  be  regarded  as  having  from  the  first 
the  form  of  a  judgment.  No  matter  how  far  one  goes  back  in  the 
history  of  consciousness,  one  will  always  find,  so  long  as  conscious- 
ness is  present  at  all,  some  reaction,  however  feeble,  upon  the 


§  74-    CONCEPTS  AND  JUDGMENTS  2/3 

content,  and  something  like  knowledge  resulting.  Even  the 
consciousness  of  the  newly  born  infant,  reacts,  or  vaguely  judges, 
in  this  way.  These  primitive  judgments  are,  of  course,  very  weak 
and  confused,  but  they  serve  as  starting-points  in  the  process  of 
intellectual  development.  Growth  in  knowledge  is  simply  the 
process  by  means  of  which  these  vague  and  inarticulate  judgments 
are  developed  and  transformed  into  a  completer  and  more  coherent 
experience. 

References 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  pp.  9-16. 
F.  H.  Bradley,  The  Principles  of  Logic,  Bk.  I.  Ch.  I. 

B.  Bosanquet,  Logic,  Vol.  I.  Ch.  I.  §§  1-6. 

H.  Lotze,  Logic  (Eng.  trans.),  Vol.  L,  pp.  13-61. 

C.  Sigwart,  Logic,  §§  40-42. 

L.  T.  Hobhouse,  The  Theory  of  Knowledge,  Pt.  I.  Chs.  I.  and  II. 


CHAPTER   XXI 

THE    MAIN    CHARACTERISTICS    OF   JUDGMENT 

§  75.  The  Universality  of  Judgments.  — We  have  now 
to  examine  the  nature  of  Judgment  a  little  more  closely 
than  we  have  done  hitherto.  And,  in  the  first  place, 
we  note  that  all  judgments  claim  universality,  There 
are,  however,  several  kinds  of  universality,  and  more 
than  one  sense  in  which  a  judgment  may  be  said  to  be 
universal.  We  speak  of  a  universal  judgment  (more 
properly  of  a  universal  proposition),  when  the  subject  is 
a  general  term,  or  is  qualified  by  some  such  word  as 
'all,'  or  'the  whole.'  And  we  distinguish  from  it  the 
particular  judgment,  where  the  subject  is  only  the  part 
of  some  whole,  and  is  usually  preceded  by  '  some,'  or  by 
other  partitive  words.  But  here  we  have  no  such  dis- 
tinction in  mind  ;  we  are  speaking  of  the  universality 
which  belongs  to  the  very  nature  of  Judgment  as  such, 
and  which  is  shared  in  by  judgments  of  every  kind. 

When  we  say  that  judgments  are  universal,  in  the 
sense  in  which  the  word  is  now  used,  we  mean  that  the 
conclusions  which  they  reach  claim  to  be  true  for  every 
one.  No  matter  what  the  subject  and  the  predicate 
may  be,  a  judgment,  e.g.,  'man  is  mortal,'  comes  forward 
as  a  fact  for  all  minds.  We  have  shown  in  the  last 
chapter  that  it  is  by  judging,  or  putting  things  together 
for  itself,  that  the  human  mind  gains  knowledge.  Now, 

274 


§  75-     THE   UNIVERSALITY   OF  JUDGMENTS  2/5 

the  assumption  upon  which  this  process  is  based  is 
that  the  result  thus  reached — knowledge — is  not  some- 
thing merely  individual  and  momentary  in  character. 
When  I  judge  that  'two  and  two  are  four/  or  that  'iron 
has  magnetic  properties/  the  judgment  is  not  merely  a 
statement  of  what  is  going  on  in  my  individual  con- 
sciousness ;  but  it  claims  to  express  something  which  is 
true  for  other  persons  as  well  as  for  me.  It  professes 
to  deal  with  facts  which  are  true,  and  in  a  sense  inde- 
pendent of  any  individual  mind.  The  judgments  by 
which  such  conclusions  are  reached  are  universal,  then, 
in  the  sense  of  being  true  for  every  one  and  at  all  times. 
The  word  'objective*  has  essentially  the  same  meaning. 
Although  each  man  reaches  truth  only  by  actually  judg- 
ing for  himself,  yet  truth  is  objective,  out  there  beyond 
his  individual  or  '  subjective  '  thought,  shared  in  by  all 
rational  beings.  The  assumption  upon  which  all  argu- 
ment proceeds  is  that  there  is  such  a  standard,  and  that 
if  people  can  be  made  to  think  they  will  arrive  at  it. 
Thought  is  objective,  or,  in  other  words,  has  in  itself 
its  own  standard  of  truth. 

The  only  alternative  to  this  position  is  scepticism,  or  pure  in- 
dividualism. If  Judgment  is  not  universal  in  the  sense  that  it 
reaches  propositions  which  are  true  for  everybody,  it  is  of  course  im- 
possible to  find  any  standard  of  truth  at  all.  The  judgments  of  any 
individual  in  that  case  would  simply  have  reference  to  what  seems 
true  to  him  at  the  moment,  but  could  not  be  taken  to  represent  any 
fixed,  or  permanent  truth.  Indeed,  if  one  regards  Judgment  as  deal- 
ing merely  with  particular  processes  in  an  individual  mind,  the 
ordinary  meanings  of  truth  and  falsehood  are  completely  lost,  and  it 
becomes  necessary  to  give  a  new  definition  of  the  words.  This  was 
the  position  of  the  Sophists  at  the  time  of  Socrates  (cf.  §  5) .  Each 


2/6       THE   MAIN  CHARACTERISTICS  OF  JUDGMENT 

individual  man  was  declared  to  be  the  measure  of  what  is  true  and 
false,  as  well  as  of  what  is  good  and  bad.  There  is  thus  no  other 
standard  of  truth  or  value  than  the  momentary  judgment  (or  ca- 
price) of  the  individual.  This  is,  in  a  way,  the  reductio  ad 
abstirdum  of  scepticism. 

The  common  nature  of  truth,  as  something  in  which  all  can 
share,  presupposes,  then,  a  common  mode  of  thinking  or  judging  on 
the  part  of  all  rational  beings.  And  it  is  this  universal  type  or  form 
of  knowing  with  which  logic  deals.  The  question  as  to  whose 
thought  is  investigated,  or  in  what  individual  mind  the  thought  takes 
place,  is  in  itself  of  no  importance.  The  consciousness  of  a  savage 
differs  very  greatly  from  that  of  an  educated  man ;  it  is  much  less 
complex  and  less  highly  developed.  But  yet,  in  spite  of  the  enor- 
mous differences,  there  exists  in  both  an  intelligence,  or  way  of 
thinking,  which  shows  the  same  essential  character,  and  operates 
according  to  the  same  fundamental  laws. 

§  76.  The  Necessity  of  Judgment.  —  The  second  char- 
acteristic which  we  note  as  belonging  to  Judgment  is 
necessity.  By  this  we  mean  that  when  a  person  judges, 
he  is  not  free  to  reach  this  or  that  conclusion  at  will. 
As  an  intellectual  being,  he  feels  bound  to  judge  in  a 
certain  way.  This  is  sometimes  expressed  by  saying 
that  we  cannot  believe  what  we  choose,  we  must  believe 
what  we  can. 

In  many  of  the  ordinary  judgments  of  everyday  life, 
which  are  made  without  any  clear  consciousness  of  their 
grounds,  logical  necessity  is  implicitly  present  as  an  im- 
mediate feeling  of  certainty.  In  cases  of  this  kind,  we 
simply  identify  ourselves  with  the  judgment,  and  feel 
that  it  is  impossible  that  it  can  be  false.  But,  of  course, 
no  judgment  can  claim  to  be  necessary  in  its  own  right. 
Its  necessity  comes  from  its  connection  with  other  facts 


§  ;6.     THE  NECESSITY  OF  JUDGMENT  277 

which  are  known  to  be  true.  Or,  in  logical  terms, 
we  may  say  that  it  comes  from  reasons  or  premises 
which  support  it.  And  one  should  always  be  ready 
to  show  the  grounds  or  reasons  upon  which  one's 
feeling  of  necessity  rests.  But  in  ordinary  life,  as  we 
have  seen,  it  is  not  unusual  to  regard  a  conclusion  as 
necessary,  without  clearly  realizing  the  nature  of  the 
reasons  by  which  it  is  supported.  An  uneducated  man 
is  rarely  able  to  go  back  and  discover  the  reasons  for 
his  belief  in  any  statement  of  which  he  is  convinced. 
If  you  question  his  assertion,  he  feels  that  you  are 
reflecting  upon  his  veracity,  and  consequently  grows 
angry.  In  the  feeling  of  immediate  necessity  or  con- 
viction, he  identifies  himself  with  the  judgment,  and 
does  not  see  that  the  criticism  is  not  directed  against 
the  latter,  but  against  the  grounds  by  which  it  is  sup- 
ported. 

In  this  distinction  between  necessity  that  is  merely 
felt,  and  the  necessity  that  is  conscious  of  its  own 
grounds,  we  see  the  direction  in  which  judgment  must 
develop.  In  the  evolution  of  thought,  we  must  become 
conscious  of  the  grounds  upon  which  our  judgments 
are  made.  That  is,  the  simple  judgment,  which  seems 
to  stand  in  isolation,  must  expand  so  as  to  unite  with 
itself  its  reasons.  By  itself,  it  is  only  a  fragment  of  a 
more  complete  and  widely  embracing  thought.  The 
feeling  of  necessity  is  an  evidence  of , its  dependence  and 
connection,  though  this  dependence  and  connection  upon 
other  facts  may  not  be  clearly  understood.  But  what 
is  implicit  must  be  made  explicit ;  the  necessity  which 
is  merely  felt  to  belong  to  the  simple  judgment  must 


2/8       THE  MAIN  CHARACTERISTICS  OF  JUDGMENT 

be  justified,  by  showing  the  grounds  or  reasons  upon 
which  it  rests.  And,  for  this  purpose,  the  simple  judg- 
ment must  expand  so  as  to  include  the  reasons  which 
are  necessary  to  support  it.  In  other  words,  it  must 
develop  into  an  inference.  As  a  matter  of  fact,  the 
same  form  of  words  as  used  by  different  persons,  or  by 
the  same  person  at  different  times,  may  express  either 
a  judgment  or  an  inference.  Thus,  '  the  price  of  wheat 
rose  after  the  war  began,'  might  express  either  a  simple 
historical  fact,  which  is  accepted  from  experience  or  from 
hearsay,  or  it  might,  in  the  mouth  of  a  person  acquainted 
with  the  laws  of  supply  and  demand,  be  the  necessary 
conclusion  of  a  number  of  premises.  Again,  a  child 
might  read  that,  'the  travellers  found  great  difficulty  in 
breathing  when  they  reached  the  top  of  the  mountain,' 
accepting  this  as  a  simple  statement  of  fact.  If  he  were 
to  read  this  same  statement  some  years  later,  however, 
he  would  probably  connect  it  at  once  with  other  facts  re- 
garding the  nature  of  the  atmosphere,  and  the  action  of 
gravity,  and  so  perceive  at  once  its  inferential  necessity. 

According  to  the  view  which  has  just  been  stated,  necessity  is  not 
a  property  which  belongs  to  any  judgment  in  itself,  but  something 
which  arises  through  its  dependence  upon  other  judgments.  In 
other  words,  necessity  is  always  mediate,  not  immediate.  This 
view,  however,  differs  from  a  theory  that  was  once  generally  received, 
and  has  some  adherents,  even  at  the  present  time,  especially  among 
thinkers  who  belong  to  the  Scottish  or  ' common-sense'  school.  In 
dealing  with  the  facts  of  experience,  we  always  explain  one  fact  by 
referring  it  to  a  second,  and  that  second  by  showing  its  dependence 
upon  some  third  fact,  and  so  on.  Thus  the  movement  of  the  piston- 
rod  in  an  engine  is  explained  by  the  pressure  of  steam,  and  this  is 
due  to  the  expansive  power  of  heat,  and  heat  is  caused  by  combus- 


§  77.    JUDGMENT  BOTH   ANALYTIC  AND   SYNTHETIC    279 

tion  of  fuel,  etc.  We  are  thus  pushed  back  in  our  explanations  from 
one  fact  or  principle  to  another,  without  ever  reaching  anything 
that  does  not  require  in  its  turn  to  be  explained. 

Now,  it  is  said  that  this  process  cannot  go  on  forever ;  for  if  it 
did  there  could  be  no  final  or  complete  knowledge;  the  whole 
system  would  be  left  hanging  in  the  air.  There  must,  therefore, 
it  is  argued,  be  some  ultimate  facts  which  furnish  the  support  for 
the  world  of  our  experience,  some  principle  or  principles  which  are 
themselves  necessary  and  do  not  require  any  proof.  That  is,  there 
must  be  certain  propositions  which  are  immediately  necessary,  and 
which  serve  as  final  explanation  for  everything  else.  Now,  it  is 
clear  that  such  propositions  must  be  entirely  different  in  character 
from  the  ordinary  facts  of  experience,  since  their  necessity  belongs 
to  their  own  nature,  and  is  not  derived  from  any  other  source.  It 
had  to  be  supposed,  therefore,  that  they  stood  upon  a  different 
plane,  and  were  not  derived  from  experience.  To  explain  the  su- 
perior kind  of  certainty  which  they  were  assumed  to  possess,  it  was 
supposed  that  they  were  present  in  the  mind  at  birth,  or  were  innate. 
They  have  also  been  called  necessary  tniths,  a  priori  truths,  and 
fundamental  Jirst  principles,  in  order  to  emphasize  their  supposed 
distinction  from  facts  which  are  derived  from  experience. 

§  77.  Judgment  involves  both  Analysis  and  Synthesis.  — 
The  business  of  our  thought  is  to  understand  the  ways 
in  which  the  various  parts  of  the  real  world  are  related. 
And  a  judgment,  as  we  have  already  seen,  is  just  a 
single  act  of  thought,  —  one  step  in  the  process  of 
understanding  the  world.  Now  we  ask:  How  does 
Judgment  accomplish  its  task?  Does  it  proceed  by 
analysis,  showing  the  parts  of  which  things  are  com- 
posed, or  does  it  employ  synthesis  in  order  to  show 
how  various  parts  combine  in  such  a  way  as  to  form 
a  whole  ?  Or  is  it  possible  for  both  these  processes  to 
be  united  in  one  and  the  same  act  of  judgment? 


280       THE  MAIN  CHARACTERISTICS  OF  JUDGMENT 

Suppose  that  one  actually  makes  the  judgment  for 
oneself  (and  does  not  merely  repeat  the  words),  '  the 
rose  has  pinnate  leaves.'  What  has  taken  place  ?  We 
notice,  firstly,  that  a  new  property  of  the  rose  has  been 
brought  to  light;  a  distinction,  or  mark,  has  been  dis- 
covered in  the  content  'rose,'  which  was  not  seen  to 
belong  to  it  before  the  judgment  was  made.  So  far, 
then,  the  process  is  one  of  analysis,  of  discovering  the 
parts  or  distinctions  of  something  which  is  at  first  taken, 
as  it  were,  in  a  lump.  And  this  is  a  most  essential  ele- 
ment in  all  thinking.  In  order  to  know,  it  is  absolutely 
necessary  that  the  differences  between  the  parts  of 
things  should  be  clearly  apprehended,  that  we  should 
not  confuse  things  which  are  unlike,  or  fail  to  make 
proper  distinctions.  If  we  examine  a  number  of  in- 
stances where  a  real  judgment  is  made,  we  shall  find 
that  this  moment  of  analysis,  or  discrimination,  is  always 
present.  Sometimes,  indeed,  analysis  may  not  seem  to 
be  the  main  purpose  of  the  judgment ;  but  if  one  looks 
closely,  one  will  always  find  in  a  judgment  that  elements 
which  are  unlike  are  held  apart  or  discriminated. 

Let  us  look  again  at  the  same  judgment,  'the  rose 
has  pinnate  leaves.'  It  is  not  difficult  to  see  that  the 
discovery  of  something  new  in  itself  is  only  one  part  of 
what  the  judgment  has  accomplished.  The  judgment 
also  affirms  the  union  of  this  new  discovery  with  the 
properties  of  what  we  call  the  rose.  It  is,  therefore, 
from  this  point  of  view,  an  act  of  synthesis.  It  asserts 
that  the  prickly  branches,  fragrant  flowers,  feather-like 
leaves,  and  other  distinctions,  are  united  in  the  one 
content  which  we  call  the  rose.  It  does  not  stop  with 


§  77-    JUDGMENT  BOTH  ANALYTIC  AND   SYNTHETIC    281 

the  mere  assertion,  '  there  is  a  mark  or  distinction,'  but 
it  affirms  that  it  is  a  mark  of  something,  i.e.,  that  it  is 
united  with  other  marks  or  properties  to  form  a  con- 
crete whole.  In  other  words,  we  may  say  that  every 
judgment  affirms  the  unity  of  the  different  parts,  or 
aspects,  of  a  thing;  and  this  is,  of  course,  synthesis. 
From  this  point  of  view,  then,  Judgment  can  be  defined 
as  a  process  of  synthesis,  just  as  we  defined  it  above  as 
one  of  analysis. 

But  how,  it  may  be  asked,  is  it  possible  for  a  judg- 
ment to  be  both  analytic  and  synthetic  ?  Are  not  these 
processes  directly  opposed  to  each  other  ?  There  can 
be  no  doubt  that  this  is  the  case  when  we  are  dealing 
with  material  things :  pulling  things  to  pieces  is  the 
opposite  of  putting  them  together.  When  we  are 
doing  the  one  we  cannot  also  be  doing  the  other.  But 
there  is  no  such  opposition  between  these  processes 
when  they  go  on  in  our  minds.  An  illustration  may 
make  this  clear.  Suppose  that  one  is  trying  to  under- 
stand some  piece  of  mechanism,  say  a  watch ;  in  order 
to  be  able  to  see  how  it  goes,  or  judge  correctly  regard- 
ing it,  two  things  are  necessary.  First,  one  must  notice 
all  the  parts  of  which  it  is  composed  —  the  wheels  of 
various  sizes,  springs,  pins,  etc.  But,  in  the  second 
place,  one  would  not  understand  the  watch  until  one 
saw  how  all  the  parts  were  united,  how  one  part  fits 
into  another,  and  all  combine  together  into  one  whole. 
We  do  not  mean  that  these  are  two  steps  which  take 
place  in  succession ;  as  a  matter  of  fact,  the  detection 
of  the  various  parts,  and  the  perception  of  their  connec- 
tion, go  hand  in  hand.  In  the  process  of  understanding 


282       THE  MAIN  CHARACTERISTICS  OF  JUDGMENT 

the  watch,  we  have  both  taken  it  to  pieces  and.  put  it 
together  again  at  one  and  the  same  time.  Not  really, 
of  course,  but  in  our  thought.  In  the  world  of  material 
things,  as  we  have  said,  only  one  of  these  processes 
could  go  on  at  a  time;  but  in  every  act  of  thinking, 
in  every  judgment,  analysis  and  synthesis  go  hand  in 
hand,  and  one  has  no  meaning  except  with  reference  to 
the  other. 

Although  every  judgment  contains,  as  we  have 
seen,  the  two  moments  of  analysis  and  synthesis,  these 
are  not  always  equally  prominent.  The  main  purpose 
of  the  judgment  usually  falls  on  one  side  or  the  other. 
In  a  judgment  like,  '  water  can  be  divided  into  hydro- 
gen and  oxygen/  the  main  emphasis  seems  to  be  on 
the  parts,  and  the  assertion  that  these  elements  are 
parts  of  a  whole,  though  present,  is  only  implied.  But 
when  one  asserts,  '  these  springs  and  wheels  together 
make  up  a  watch/  it  is  the  nature  of  the  whole  upon 
which  the  emphasis  is  laid,  and  the  separation  or  dis- 
crimination of  the  parts,  is,  as  it  were,  secondary.  It  is 
not  difficult  to  see,  however,  that  the  two  moments  of 
Judgment  are  present  in  both  of  these  cases.  The  dif- 
ference consists  in  the  fact  that  at  one  time  analysis, 
and  at  the  other  synthesis,  is  made  the  main  purpose. 

It  was  at  one  time  supposed  that  analytic  and 
synthetic  judgments  were  entirely  different  in  kind 
from  each  other.  An  analytic  judgment,  it  was  said, 
is  one  in  which  the  predicate  is  obtained  by  analyzing, 
or  bringing  to  light,  what  is  contained  in  the  subject. 
Thus  the  judgment,  'all  material  bodies  fill  space/  is 
analytic ;  for  the  predicate  (space-filling)  is  contained  in 


§  77.    JUDGMENT  BOTH   ANALYTIC  AND   SYNTHETIC     283 

the  very  notion,  or  idea,  of  a  material  body.  All  that 
is  necessary  in  order  to  obtain  the  judgment  is  to  com- 
prehend the  meaning  of  the  subject.  An  analytic  judg- 
ment, then,  adds  nothing  to  our  knowledge.  It  merely 
enables  us  to  bring  to  light  and  express  what  is  con- 
tained in  the  ideas  we  already  possess.  A  synthetic 
proposition,  on  the  contrary,  was  defined  as  one  in  which 
the  predicate  was  not  already  contained  in  the  subject, 
but  which  added  a  new  element  or  idea  to  it.  '  This  body 
weighs  ten  pounds/  for  example,  is  a  synthetic  propo- 
sition, for  one  cannot  obtain  the  predicate  by  analyzing 
the  subject.  The  predicate  adds  a  new  fact  which 
must  have  been  derived  from  experience. 

This  view  is  of  course  fundamentally  different  from  the  account 
of  Judgment  which  we  have  just  given.  The  absolute  distinction 
between  analytic  and  synthetic  judgments,  like  the  theory  that 
thought  begins  with  concepts,  arises,  I  think,  from  a  substitu- 
tion of  the  spoken  or  written  proposition  for  the  judgment  itself. 
In  the  proposition  the  subject  seems  to  be  the  starting-point.  We 
have  a  word  or  term  which  appears  to  be  independent  and  capa- 
ble of  standing  alone.  The  question  is,  then,  where  shall  we  find 
the  predicate  ?  For  example,  in  the  proposition,  '  iron  is  an  ele- 
ment,' the  subject  stands  first,  and  the  predicate  comes  later.  It 
seems  possible  then  to  say  that  we  have  first  the  subject  i  iron,'  and 
then  join  on  to  it  the  predicate  l  element,'  which  has  been  obtained 
either  by  analyzing  the  subject,  or  from  some  previous  experience. 
But  the  proposition,  as  a  collection  of  words,  must  not  be  substituted 
for  the  act  of  judgment.  Judgment,  as  we  have  already  seen,  is  a 
single  act  of  intelligence,  which  at  once  discriminates  and  brings 
into  relation  different  aspects  of  the  whole  with  which  it  is  dealing. 
A  mere  subject  by  itself  has  not  any  intelligible  meaning.  If  one 
hears  the  word  '  iron,'  for  example,  the  word  may  call  up  certain 
mental  images ;  but  by  itself  it  is  not  a  complete  thought  or  fact  in 


284       THE  MAIN  CHARACTERISTICS  OF  JUDGMENT 

which  we  can  rest.  t  Well,  what  of  it?  '  we  say.  The  mind  at  once 
goes  on  to  form  some  judgment  like,  'this  is  iron,1  or  ;  iron  is  heavy.' 
We  cannot  think  a  term  without  thinking  something  of  it.  In  short, 
although  the  words  which  form  the  subject  of  a  proposition  are 
relatively  independent,  and  can  be  used  without  the  words  which 
make  up  the  predicate,  in  a  judgment,  on  the  other  hand,  a  subject 
is  only  a  subject  through  its  relation  to  a  predicate.  The  propo- 
sition may  be  divided  into  parts,  but  the  judgment  is  a  single 
thought-activity,  and  cannot  be  divided  (cf.  §  74). 


§  78.  Judgment  as  Constructing  a  System  of  Knowledge. 

In  this  section  we  have  not  to  take  account  of  any  new 
characteristic  of  Judgment,  but  rather  to  emphasize 
the  part  it  plays  in  building  up  knowledge.  As  we 
have  seen,  Judgment  works  both  analytically  and  syn- 
thetically :  it  discovers  new  parts  and  distinctions,  and 
at  the  same  time  brings  the  parts  into  relation  and  thus 
builds  up  a  whole.  That  is  the  law  according  to  which 
thinking  develops,  and  is  just  what  we  called  differen- 
tiation and  integration  in  a  previous  section  (§  72). 

It  is  necessary  here,  however,  to  dwell  upon  the  fact 
that  each  judgment  may  be  regarded  as  a  step  in  the 
process  of  building  up  a  system  of  knowledge.  The 
emphatic  word  here  is  'system,'  and  we  must  be  per- 
fectly clear  about  its  meaning.  A  system  is  a  whole 
which  is  composed  of  various  parts.  But  it  is  not  the 
same  thing  as  an  aggregate  or  heap.  In  an  aggregate 
or  heap,  no  essential  relation  exists  between  .the  units 
of  which  it  is  composed.  In  a  heap  of  grain,  or  pile  of 
stones,  one  may  take  away  any  part  without  the  other 
parts  being  at  all  affected  thereby.  But  in  a  system, 
each  part  has  a  fixed  and  necessary  relation  to  the  whole 


§  78.    CONSTRUCTING  A  SYSTEM   OF  KNOWLEDGE    285 

and  to  all  the  other  parts.  For  this  reason  we  may  say 
that  a  building,  or  a  piece  of  mechanism,  is  a  system. 
Each  stone  in  the  building,  each  wheel  in  the  watch, 
plays  a  part,  and  is  essential  to  the  whole.  In  things 
which  are  the  result  of  growth,  the  essential  relations  in 
which  the  parts  stand  is  even  more  clearly  evident. 
The  various  parts  of  a  plant  or  an  animal  have  each  their 
own  function,  but  at  the  same  time  they  are  so  neces- 
sary to  each  other  that  an  injury  to  one  is  an  injury  to 
all.  We  express  this  relation  in  the  case  of  living  things 
by  saying  that  the  parts  are  organic  to  each  other.  And, 
in  the  same  way,  it  is  not  unusual  to  speak  of  society  as 
an  organism,  in  order  to  express  the  fact  that  the  vari- 
ous individuals  of  which  it  is  composed  are  not  inde- 
pendent units,  but  stand  in  necessary  relations  to  one 
another,  and  are  all  mutually  helpful  or  hurtful. 

We  have  said  that  Judgment  constructs  a  system  of 
knowledge.  This  implies,  then,  that  it  is  not  merely 
a  process  of  adding  one  fact  to  another,  as  we  might 
add  one  stone  to  another  to  form  a  heap.  No  !  Judg- 
ment combines  the  new  facts  with  which  it  deals,  with 
what  is  already  known,  in  such  a  way  as  to  give  to 
each  its  own  proper  place.  Different  facts  are  not 
only  brought  together,  but  they  are  arranged,  related, 
systematized.  No  fact  is  allowed  to  stand  by  itself,  but 
has  to  take  its  place  as  a  member  of  a  larger  system 
of  facts,  and  receive  its  value  from  this  connection.  Of 
course,  a  single  judgment  is  not  sufficient  to  bring  a 
large  number  of  facts  into  relation  in  this  way.  But  each 
judgment  contributes  something  to  this  end,  and  brings 
some  new  fact  into  relation  to  what  is  already  known. 


286       THE   MAIN   CHARACTERISTICS   OF  JUDGMENT 

In  a  simple  judgment  like,  'that  was  the  twelve  o'clock 
whistle,'  the  constructive  or  systematizing  work  accom- 
plished is  evident.  The  auditory  sensation,  which  in 
itself,  as  a  mere  wandering  sound,  was  not  a  piece  of 
knowledge  at  all,  is  interpreted  in  such  a  way  as  to  find 
a  place  in  the  system  of  experience.  One  may  appreciate 
what  part  the  judgment  really  plays  by  remembering  how 
the  sound  appeared  before  one  was  able  to  judge.  There 
may  have  been  at  first  a  moment  of  bewilderment — 
'  What  does  this  mean  ? '  one  asks.  In  the  next  moment 
the  judgment  is  made :  '  It  is  the  twelve  o'clock  whistle/ 
That  is,  our  thinking  has  constructed  a  meaning  for  it, 
and  brought  it  into  relation  with  the  rest  of  our  know- 
ledge. 

(i)  Every  new  experience  is  thus  brought  into  relation  with  the 
facts  which  we  already  know,  and  is  tested  by  them.  It  has  to  find  its 
place  in  the  system  of  knowledge  —  to  join  itself  to  what  is  already 
known.  If  this  is  impossible,  if  what  claims  to  be  a  fact  is  entirely 
opposed  to  what  we  already  know  on  the  same  subject,  it  is  usually 
declared  to  be  false.  Thus,  we  would  refuse  to  believe  that  some 
person  whom  we  know  well  and  respect  was  guilty  of  theft ;  for  it 
would  be  impossible  to  connect  such  conduct  with  what  we  already 
know  of  his  character.  And,  similarly,  we  find  it  impossible  to 
believe,  even  although  we  have  the  evidence  of  our  senses,  that  the 
conjurer  has  actually  performed  what  he  professes;  for  to  do  so 
would  often  be  to  reverse  entirely  our  conception  of  natural  laws.  It 
must  not  be  forgotten,  however,  that  the  existing  system  of  know- 
ledge, which  seems  to  serve  as  the  standard  and  test  of  new  facts,  is 
itself  undergoing  constant  modification  through  the  influence  of 
these  facts.  As  new  experiences  are  brought  into  connection  with 
the  existing  body  of  our  knowledge,  there  is  a  constant  rearrange- 
ment and  readjustment  of  the  latter  going  on.  Usually  this  adjust- 
ment is  slight,  and  takes  place  almost  imperceptibly.  But,  in  some 


§  78.    CONSTRUCTING  A   SYSTEM   OF  KNOWLEDGE    287 

cases,  a  single  fact  may  be  so  significant  as  completely  to  transform 
what  seemed  to  be  the  accumulated  knowledge  of  years.  The 
experiment  which  Galileo  made  by  dropping  balls  of  different 
weight  from  the  tower  of  Pisa,  made  it  impossible  to  hold  any  longer 
the  old  theory  —  which  seemed  as  certain  as  anything  well  could  be 
—  that  the  velocity  with  which  bodies  fall  is  proportional  to  their 
weight.  Again,  if  theft  were  actually  proved  against  the  man  we 
respect,  that  single  fact  might  be  sufficient  to  force  us  to  give  up 
everything  which  we  supposed  that  we  knew  about  his  character. 

(2)  We  have  said  that  judgment  is  the  process  by  which  know- 
ledge grows  into  a  system.  It  is  by  judging  or  thinking  that  we 
attempt  to  bring  the  various  parts  of  our  experience  into  relation 
with  one  another.  The  degree  to  which  this  has  been  done  is  the 
measure  of  our  intellectual  development.  The  knowledge  of  the 
uneducated  and  unthinking  man,  like  that  of  the  child,  is  largely 
composed  of  unrelated  fragments.  It  is  an  aggregation,  not  a 
system  of  facts.  The  facts  which  go  to  make  it  up  may  quite  well 
be  contradictory,  but  this  contradiction  is  not  seen  because  no 
attempt  is  made  to  unite  them.  There  is,  of  course,  no  human 
experience  which  is  entirely  systematic,  or  which  has  been  com- 
pletely unified.  Even  those  who  have  thought  most  deeply  find  it 
impossible  to  fit  together  exactly  knowledge  gained  from  different 
fields,  and  from  different  sciences.  The  facts  of  one  science,  for 
example,  may  seem  to  stand  by  themselves,  and  not  to  have  any 
relation  to  the  facts  derived  from  another  science.  Or  there  may 
appear  to  be  a  conflict  between  the  results  of  physical  sciences, 
and  the  truths  of  moral  philosophy  and  religion.  But  the  ideal 
always  remains  that  truth  is  one  and  indivisible,  and  that  it  must 
be  possible  ultimately  to  harmonize  all  facts  in  one  all-embracing 
system  of  judgment. 

References 

B.  Bosanquet,  The  Essentials  of  Logic,  Lecture  II. 
"  «          Logic,  Vol.  I.,  pp.  97-103. 

C.  Sigwart,  Logic,  §  18. 


CHAPTER   XXII 

THE    LAWS    OF    THOUGHT 

§  79.  The  Law  of  Identity.  —  We  found  (§  73)  that 
Judgment  is  the  simplest  form  of  thinking.  And,  in 
the  last  chapter,  we  were  engaged  in  studying  its  main 
characteristics,  and  becoming  acquainted  with  its  mode 
of  operation.  The  essential  nature  of  the  thinking 
process,  therefore,  has  already  been  stated,  though  we 
have  not  traced  the  mode  of  its  development,  nor  shown 
its  application  to  the  various  problems  of  experience.  In 
nearly  all  books  dealing  with  logic,  however,  one  finds  a 
statement  of  three  fundamental  laws  of  thought  which 
differ  greatly,  in  form  at  least,  from  what  we  have  so 
far  learned  regarding  the  nature  of  Judgment.  These 
laws  are  so  well  known  by  name,  and  yet  so  ambiguous 
in  their  mode  of  statement,  that  it  seems  well  to  try  to 
decide  what  meaning  to  apply  to  them.  It  will  also  be 
interesting  to  note  their  relation  to  the  discussion  of 
Judgment  already  given.  They  are  usually  regarded  as 
axioms,  or  propositions  which  require  no  proof,  rather 
than  as  descriptive  of  the  nature  of  thought.  In  this 
sense,  they  are  supposed  to  be  the  foundation  of  all 
logic,  since  they  are  presupposed  in  all  thinking. 

The  first  of  these  laws,  or  axiomatic  principles,  is  that 
of  Identity.  Whatever  is,  is  ;  everything  remains  iden- 
tical with  itself ;  A  is  A.  These  are  some  of  the  forms 
in  which  the  law  is  usually  stated.  In  all  argument,  we 

288 


§  79-     THE  LAW  OF  IDENTITY  289 

assume  at  least  that  each  thing  possesses  a  permanent 
character,  and  does  not  pass  now  into  this,  now  into 
that.  If  any  knowledge  is  to  be  possible  at  all,  the 
character  of  things  must  remain  fixed.  Socrates  is 
always  to  be  Socrates,  and  iron,  iron.  Every  one  as- 
sumes as  much  as  this,  though  he  may  not  himself  be 
conscious  of  it  (cf.  §  9). 

Another  interpretation  of  this  principle  was,  how- 
ever, offered  by  Boole  and  Jevons,  who  developed  what 
is  known  as  the  Equational,  or  Symbolic  logic.  Accord- 
ing to  these  writers,  the  law  of  Identity  expresses 
the  fundamental  nature  of  Judgment.  That  is  to  say, 
every  judgment  is  the  expression  of  an  identity  between 
the  subject  and  the  predicate.  The  judgment,  'New 
York  is  the  largest  city  in  America,'  is  simply  a  case  of 
a  is  a.  It  expresses  the  fact,  that  is,  that  New  York 
and  the  largest  city  in  America  are  identical.  '  Iron  is 
a  metal,'  is  another  example  of  the  same  principle.  It 
may  be  written :  iron  =  metal.  And,  since  the  copula 
may  often  be  ambiguous,  it  will  be  better  to  discard  it 
in  working  out  arguments,  and  adopt,  in  its  place,  the 
sign  of  equality. 

Judgment,  then,  is  simply  an  equation,  and  may  be 
written  as  such.  Further,  the  conclusion  of  a  series  of 
logical  premises  may  be  obtained  by  a  process  similar 
to  that  employed  in  working  algebraical  equations. 
That  is,  we  can  substitute  for  any  term  in  a  judgment, 
its  equivalent,  or  the  value  which  it  has  in  another 
judgment.  This  method  Jevons  calls  '  the  substitution 
of  similars,'  which  he  maintains  is  the  fundamental 
principle  of  all  reasoning. 


2QO  THE  LAWS   OF  THOUGHT 

If,  now,  we  employ  letters  to  symbolize  the  terms  of 
the  propositions,  it  is  claimed  that  we  can  work  out 
any  argument  by  the  equational  method.  Take  the 
argument, 

All  metals  are  elements, 

Iron  is  a  metal, 

Therefore  iron  is  an  element. 

Now  represent  metal  by  M  ;  iron  by  I ;  and  element  by 
E.     Then  the  argument  in  equational  form  will  be, 

M  =  E (i) 

I  =  M (2) 

and  by  the  substitution  in  (i)  of  the  value  of  M  in  (2) 
we  get  I  =  E,  the  required  conclusion. 

Or,  we  may  illustrate  this  method  by  a  somewhat 
more  complex  example  which  is  also  taken  from  Jevons  : 
'  Common  salt  is  sodium  chloride,  which  is  a  substance 
that  crystallizes  in  cubical  form ;  but  what  crystallizes 
in  cubical  form  does  not  possess  the  power  of  double 
refraction.'  The  conclusion  of  this  argument  may  be 
found  by  letting  A  =  Common  Salt,  B  =  Sodium  Chlo- 
ride, C  =  something  which  crystallizes  in  cubical  form, 
and  D  =  something  which  possesses  the  power  of  double 
refraction.  The  negative  of  any  of  these  terms  will  be 
expressed  by  the  corresponding  small  letters.  The  argu- 
ment may  now  be  expressed  :  — 

A  =  B (i) 

B  =  C (2) 

C  =  d (3) 

By  substitution  of  the  value  of  C  in  (2)  we  get, 

B  =  d (4) 

And  substituting  here  the  value  qf  B  in  (i), 


§  79-    THE  LAW  OF  IDENTITY  29 1 

Giving  to  these  symbols  their  meanings,  we  get  the 
result  '  common  salt  does  not  possess  the  power  of 
double  refraction,'  which  is  the  conclusion  of  the  argu- 
ment. 

Of  course,  in  simple  arguments  like  those  we  have 
been  examining,  there  is  nothing  gained  by  the  use 
of  symbols,  and  the  representation  of  arguments  in 
this  form.  But  when  the  various  terms  employed  are 
much  longer  and  more  complex,  simplification  may  be 
attained  in  this  way.  Various  other  symbols  have  also 
been  used  to  express  the  relation  of  the  various  terms 
to  each  other,  and  a  symbolic  logic  has  been  developed 
which  follows  very  closely  the  procedure  of  algebra. 
The  examples  given  may,  however,  serve  as  illustrations 
of  this  method. l 

It  is,  however,  as  a  theory  of  the  meaning  of  Judg- 
ment that  we  are  interested  in  this  mode  of  interpreting 
the  law  of  Identity.  We  have  seen  that  it  works  fairly 
well  in  practice,  and  therefore  cannot  be  wholly  false. 
But  there  are  certain  forms  of  reasoning  in  which  it  will 
not  work.  We  cannot  get  the  conclusion  by  the  equa- 
tional  method  in  an  example  like  the  following :  '  B  is 
greater  than  A,  C  is  greater  than  B,  therefore  C  is  still 
greater  than  A.' 

This  practical  objection  being  left  out  of  account,  we 
have  to  ask  whether  an  equation  represents  fairly  the 
nature  of  Judgment.  Does  a  judgment  express  merely 

1The  clearest  statement  of  the  aims  and  methods  of  the  Equational 
Logic  may  perhaps  be  obtained  from  Jevons,  The  Principles  of  Science, 
Introduction.  Cf.  also  G,  Boole,  An  Investigation  of  the  Laws  of  Thought. 
London,  1854. 


292  THE  LAWS   OF  THOUGHT 

the. identity  of  subject  and  predicate  ?  And  if  so,  what 
kind  of  identity  is  referred  to  ?  In  mathematical  rea- 
soning, the  sign  of  equality  expresses  the  identity  of 
quantitative  units.  When  one  says,  2  +  3  =  5,  the 
meaning  is  that  the  number  of  units  on  each  side  of 
the  equation  is  identical.  And,  similarly,  the  assertion 
that  a  parallelogram  =  2  triangles  with  the  same  base 
and  of  the  same  altitude  as  itself,  expresses  the  fact  that, 
in  the  two  cases,  the  number  of  units  of  area,  square 
feet,  square  yards,  etc.  is  the  same.  In  mathematics,  the 
equation  declares  that  the  quantitative  relations  of  its 
two  sides  are  identical.  It  does  not  assert  that  the  two 
things  compared  —  the  triangle  and  one  half  the  par- 
allelogram, for  example  —  have  the  same  qualities,  or 
are  exactly  the  same  in  all  respects.  Now,  if  we  ex- 
tend the  use  of  the  sign  of  equality,  it  must  take  on 
a  new  meaning.  It  is  clear  that  in  a  judgment  like 
'iron  =  metal,'  there  is  no  reference  at  all  to  quantita- 
tive relations.  We  are  not  asserting  that  the  number 
of  units  in  the  two  terms  is  identical.  What,  then,  does 
the  sign  of  equality  express  in  such  a  case? 

The  answer  is  not  difficult,  say  those  who  hold  this 
theory.  The  sign  of  equality  in  such  cases  expresses 
absolute  identity ;  the  entire  and  complete  sameness  of 
subject  and  predicate.  The  proposition,  *  mammals  = 
vertebrates,'  asserts  that  mammals  and  vertebrates  are 
one  and  the  same  thing.  But  that  statement  in  its 
present  form  is  not  true :  the  class  mammal  does  not 
completely  correspond  with  the  class  vertebrate.  To 
make  it  exact,  say  those  who  uphold  the  equational 
form,  one  must  qualify  or  limit  the  predicate  and  write 


§  79-    THE  LAW  OF  IDENTITY  293 

the  proposition,  '  mammals  —  some  vertebrates.'  But, 
even  so,  we  may  urge,  the  form  of  the  judgment  is  still 
defective.  In  the  first  place,  it  does  not  correspond  to 
the  model  a  =  a.  For  one  side,  ( mammal/  is  clearly 
marked  off,  while  the  other  is  indefinite  and  vague. 
And,  secondly,  just  because  of  its  vagueness,  it  is  not 
a  satisfactory  piece  of  knowledge.  To  obviate  these 
objections,  one  must  go  further  and  write,  mammals  = 
mammalian  vertebrates.  At  last  the  judgment  seems 
to  correspond  to  the  type,  a  =  a.  But  a  new  difficulty 
arises.  Has  not  the  judgment  lost  all  its  original  mean- 
ing and  become  a  mere  tautology  ?  There  seems  to  be 
no  escape  from  the  following  dilemma :  either  there  is 
some  difference  between  subject  and  predicate,  and  the 
judgment  is  therefore  not  in  the  form  a  =  a,  or  the  judg- 
ment is  tautologous  and  expresses  nothing.  The  view 
of  the  equational  logic  that  Judgment  affirms  the  entire 
identity  of  subject  and  predicate  refutes  itself.  The 
form  a  =  a  cannot  be  regarded  as  the  type  to  which  all 
judgments  conform. 

But  there  must  be  some  kind  of  identity  between  the 
parts  of  a  judgment.  In  one  sense,  we  do  seem  to 
declare  that  the  subject  and  predicate  are  identical 
when  we  say,  'iron  is  a  metal.'  As  we  have  seen,  how- 
ever, if  these  terms  are  merely  identical  and  nothing 
more,  the  judgment  loses  all  meaning.  We  are  forced 
to  the  conclusion  that  every  judgment  affirms  both 
identity  and  difference,  or  that  there  is  identity  running 
through  and  underlying  the  diversity.  But  is  not  this 
a  paradoxical  statement  ?  When  we  affirm  identity, 
does  not  this  imply  the  absence  of  all  difference?  If 


294  THE  LAWS  OF  THOUGHT 

a  is  a,  how  can  it  at  the  same  time  be  something  differ- 
ent from  itself  ? 

And  yet  this  is  just  what  every  judgment  which  has 
any  meaning  affirms.  'Iron  is  fusible/  'This  table  is 
made  of  oak.'  'The  sword  is  rusty  with  age.'  In  all 
these  judgments  there  is  an  assertion  of  the  unity  of 
different  properties  or  parts  in  one  whole.  A  is  B,  and 
yet  does  not  cease  to  be  A,  is  rather  the  type  of  judg- 
ment than  a  is  merely  or  abstractly  a.  It  is  worth 
noticing  that  this  view  of  the  matter  corresponds  with 
the  account  of  Judgment  already  given.  We  saw 
that  Judgment  constructs  a  system  of  knowledge  by 
showing  that  various  things,  which  seem  at  first  unre- 
lated, are  yet  connected  by  an  underlying  unity.  Know- 
ledge is  always  the  synthesis  or  union  of  different  parts 
or  different  properties  in  a  common  identity.  And 
each  judgment,  as  an  element  of  knowledge,  displays 
the  same  essential  structure  which  belongs  to  knowledge 
as  a  whole.  It  involves,  as  was  shown  in  (§  77),  both 
analysis  and  synthesis,  and  declares  the  oneness  or 
identity  of  a  number  of  properties  or  parts,  without  at 
the  same  time  losing  sight  of  their  distinctness. 

Let  us  now  sum  up  our  discussion  of  the  law  of  Iden- 
tity. When  rightly  understood,  as  we  have  seen,  it  does 
not  affirm  that  a  can  only  be  bare  a,  that  the  subject 
and  predicate  are  absolutely  identical.  It  is  a  law  of 
thought,  and  expresses  the  fact  that  Judgment  brings 
together  differences  ;  i.e.,  different  things  and  qualities, 
and  shows  that  they  are  parts  of  one  whole  or  unity. 
It  reveals  the  underlying  unity  or  identity  which  is 
present  in  the  midst  of  variety.  This  law  also  states 


§  8o.    THE   LAW   OF   CONTRADICTION  2Q5 

another  characteristic  of  Judgment  which  we  have 
already  emphasized.  This  is  what  we  have  called  the 
universality  of  Judgment  (§  75).  It  is  to  judgments,  and 
not  to  concepts  or  terms,  as  has  sometimes  been  sup- 
posed, that  the  law  of  Identity  properly  applies.  What 
it  affirms  in  this  connection  is  simply  that  Judgment 
claims  to  be  true,  and  hence  is  identical  at  all  times 
and  for  all  persons.  It  cannot  be  true  for  you  and 
false  for  me  that,  'iron  is  a  metal.'  Truth  is  not  a 
matter  of  individual  taste,  but  every  judgment  which 
is  true  has  a  permanent  character  or  identity  belonging 
to  it. 

§  80.  The  Law  of  Contradiction.  — The  law  of  Contra- 
diction is  the  second  of  the  so-called  laws  of  thought. 
It  is  usually  stated  as  follows :  It  is  impossible  for  the 
same  thing  both  to  be  a,  and  not  to  be  a ;  or,  a  is  not 
not-a.  It  is  evident  that  this  law  states  in  a  negative 
form  the  same  characteristics  of  thought  as  the  law  of 
identity.  Indeed,  it  was  in  this  form  that  the  principle 
was  first  laid  down  by  Aristotle.  "It  is  impossible," 
he  says,  "that  the  same  predicate  can  both  belong  and 
not  belong  to  the  same  subject  at  the  same  time,  and 
in  the  same  sense."  1  We  cannot  assert  in  the  same 
sense  that  Socrates  is  both  wise,  and  not  wise.  Truth 
is  not,  as  the  Sophists  supposed,  a  matter  of  taste  or 
convenience,  but  must  be  consistent  with  itself.  If  a 
judgment  affirms  that  'iron  is  a  metal/  it  at  the  same 

1  Metaphysics,  Bk.  III.  Ch.  IV.  See  also  the  remaining  chapters  of 
the  same  book  for  Aristotle's  demonstration  that  all  thought  presupposes 
such  a  principle. 


296  THE  LAWS  OF  THOUGHT 

time  excludes  the  assertion  that  it  is  not  a  metal. 
There  is  a  fixity  and  permanence  about  judgments 
which  prevents  them  from  changing  into  anything  else. 
And  it  is  just  this  permanence  which  we  have  already 
called  the  universality  of  Judgment,  which  the  law  of 
Contradiction  expresses  in  a  negative  form. 

The  law  of  Contradiction  has,  however,  sometimes 
been  interpreted  in  such  a  way  as  to  make  it  equivalent 
to  the  assertion  of  abstract  or  bare  identity  which  we 
found  in  the  Equational  logic.  That  is,  the  statement 
that  it  is  impossible  for  any  judgment  to  unite  a  and 
not-a  may  be  taken  to  mean  that  it  is  impossible  to 
assert  the  unity  of  a  and  anything  different  from  a. 
But,  as  we  have  seen,  this  is  exactly  what  we  do  in 
every  judgment  which  is  more  than  a  tautology.  The 
law,  then,  does  not  forbid  the  union  of  differences  in 
one  judgment,  but  of  contradictories,  or  of  what  would 
destroy  the  integrity  of  the  judgment  and  render  it 
unmeaning.  If  the  law  is  to  hold  true  of  Judgment, 
not-a  must  not  be  taken  as  equivalent  to  anything  which 
is  different  from  a,  but  as  signifying  what  is  opposed,  or 
contradictory  to  a. 

It  is  not  by  any  means  easy  to  decide  what  things  are  merely 
different,  and  therefore  compatible  with  each  other,  and  what  con- 
tradictory or  opposed.  Logic  can  give  no  rule  which  may  be  applied 
in  every  case.  If  experience  shows  that  two  things,  or  two  proper- 
ties, are  at  any  time  united,  we  say  that  they  are  merely  different 
from  each  other ;  if  they  have  never  been  found  in  conjunction  and 
we  are  not  able  to  conceive  how  their  union  could  take  place,  we 
call  them  opposites  or  contradictories.  It  is  worth  noticing,  too, 
that  no  terms  are  in  themselves  contradictory,  except  those  which 
are  in  the  form  a  and  not-a,  wise  and  not- wise.  But  they  become 


§  8i.  THE  LAW  OF  EXCLUDED  MIDDLE     297 

contradictory  and  exclude  each  other  when  they  claim  to  occupy 
the  same  place  in  some  particular  system  of  facts.  Thus  '  maple ' 
and  i  oak '  denote  trees  of  a  different  variety,  which  are,  however,  so 
little  opposed  that  they  may  exist  side  by  side.  If  both  these  terms 
were  applied  to  the  same  tree,  however,  they  would  become  con- 
tradictory. By  claiming  to  stand  in  the  same  relations,  these 
terms  become  rivals,  as  it  were,  and  exclude  each  other.  But  a 
knowledge  of  the  particular  facts  involved  is  always  necessary 
in  order  to  determine  whether  or  not  two  assertions  are  really 
incompatible. 


§  8 1.  The  Law  of  Excluded  Middle.  —The  third  law  is 
a  corollary  from  what  has  just  been  said  in  the  last  sec- 
tion. There  is  no  middle  ground,  it  declares,  between 
contradictories.  A  is  either  b  or  not-b.  To  affirm  the 
one  is  to  deny  the  other.  When  we  have  real  contra- 
dictories,—  i.e.,  when  not-b  is  not  merely  something 
different  from  b,  but  something  which  excludes  it, — 
every  judgment  is  double-edged,  and  both  affirms  and 
denies  at  the  same  time.  To  deny  that  the  throw  of  a 
penny  has  given  heads,  is  to  assert  that  it  has  fallen 
tails.  As  we  have  seen,  however,  logic  affords  no  rules 
of  deciding  when  things  do  thus  stand  in  the  relation 
of  mutual  opposition.  The  law  of  Excluded  Middle 
states  only  that  where  this  relation  does  exist,  every 
proposition  has  a  double  value,  and  both  affirms  and 
denies  at  the  same  time.  It  requires  special  know- 
ledge of  the  particular  facts  in  each  case  to  enable 
us  to  decide  what  things  are  thus  opposed  to  one 
another.  There  is  no  logical  law  by  means  of  which 
things  may  be  divided  into  two  opposing  groups  or 
classes. 


298  THE  LAWS  OF  THOUGHT 

It  is  important  to  notice  that  all  of  the  judgments 
which  we  use  in  everyday  life  are  to  some  extent  double- 
edged.  That  is,  they  contain,  besides  what  is  directly 
affirmed,  some  implication  or  counter  statement.  For 
example,  to  say,  'that  object  is  red/  is  implicitly  to  deny 
that  it  is  blue,  or  any  other  colour.  The  statement,  '  A 
never  looks  at  a  book,'  carries  with  it  the  implication 
that  A  is  not  very  intelligent.  In  almost  any  field 
where  we  have  any  systematic  knowledge,  we  can  limit 
pretty  definitely  the  number  of  possibilities  —  a  must 
be  either  by  or  c,  or  d.  In  such  cases,  to  affirm  that  a  is 
b,  is  of  course  to  deny  implicitly  c  and  d ;  and  con- 
versely, the  denial  of  any  one  possibility,  as  c,  enables 
one  to  assert  that  a  is  b  or  d.  In  ordinary  conversa- 
tion, misunderstandings  and  misconceptions  frequently 
arise  because  neither  party  is  fully  aware  of  all  the  pos- 
sible cases  and  the  relation  between  them.  It  is  very 
difficult,  however,  to  make  a  statement  which  will  have 
no  counter  implications.  If  one  says,  '  this  railway  sys- 
tem does  not  employ  steam  power,'  the  proposition 
seems  to  justify  the  question:  'Does  it  then  use  elec- 
tricity or  compressed  air  ? '  We  should  feel  that  it  was 
a  mere  quibble  if  the  person  who  made  the  statement 
should  reply :  '  I  did  not  say  that  it  employed  any  kind 
of  power.'  'There  are  some  small  errors  in  this  paper,' 
would  ordinarily  be  taken  to  imply  the  counter  propo- 
sition, 'the  paper  contains  no  serious  errors.'  It  is 
clear  that  it  is  only  when  one's  knowledge  becomes 
systematic,  —  i.e.,  when  one  knows  the  relations  in 
which  all  the  facts  in  the  field  under  consideration 
stand  to  each  other,  —  that  one  can  be  fully  aware 


§  8i.    THE  LAW  OF  EXCLUDED   MIDDLE  299 

of  what  is  really  implied   in  each  assertion  or  denial 
(cf.  §§  41,  78).    ' 

References 

F.  H.  Bradley,  The  Principles  of  Logic,  pp.  131-154,  343-360. 

B.  Bosanquet,  Logic,  Vol,  II.,  pp.  207-212. 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  Ch.  XIV. 
"     "        "        The  Principles  of  Science,  Introduction. 

G.  T.  Ladd,  The  Philosophy  of  Knowledge,  Ch.  IX. 

C.  Sigwart,  Logic,  §§  23-25. 

J.  Watson,  "  The  Metaphysic  of  Aristotle,"  Philos.  Review,  Vol 
VII.,  pp.  113-134- 


CHAPTER   XXIII 

TYPES    OF   JUDGMENT 

§  82.  Judgments  of  Quality.  —  We  have  hitherto  been 
considering  the  nature  of  Judgment  in  general,  and 
have  learned  something  regarding  its  main  character- 
istics. It  is  now  necessary  to  examine  briefly  some  of 
the  more  important  forms  or  types  of  Judgment.  We 
shall  begin  with  very  simple  and  elementary  ways  of 
judging,  and  afterwards  consider  some  of  the  more 
complex  types.  In  this  way,  we  shall,  see  the  nature 
and  structure  of  Judgment  illustrated  at  different  levels 
of  thought.  And  we  also  hope  to  show  that  there  are 
no  arbitrary  divisions  in  the  process  of  thinking,  that 
the  lower  forms  of  Judgment  gradually  develop  into  the 
higher  in  accordance  with  the  general  law  of  evolution. 
It  is,  of  course,  impossible  to  carry  out  at  present  this 
plan  in  detail,  for  that  would  be  to  give  a  complete  his- 
tory of  the  development  of  thought.  It  will  be  neces- 
sary for  us  to  take  long  steps,  and  content  ourselves 
with  a  general  view  of  the  relation  of  the  various  stages 
in  the  development  of  Judgment. 

The  first  efforts  of  intelligence  to  understand  the 
world  take  the  form  of  judgments  of  Quality.  At  a  low 
stage  of  mental  development,  it  is  the  simple  qualities 
of  things  which  force  themselves  on  attention.  The 
young  child,  for  example,  takes  notice  of  only  the 

300 


§  82.    JUDGMENTS   OF  QUALITY  301 

most  striking  qualities  of  things.  His  judgments  are 
very  vague  and  indefinite,  and  take  account  only  of 
some  prominent  quality  of  things.  That  is,  there  is  no 
discrimination  of  the  various  parts  and  relations  of  the 
objects,  but  the  judgments  express  merely  a  general 
impression  based  upon  some  striking  quality.  Thus  it 
has  often  been  noticed  that  the  child  calls  every  man 
'papa,'  and  any  light,  of  whatever  size,  the  moon.  A 
little  boy,  known  to  the  author,  used  to  call  Sisters 
of  Charity,  crows,  on  account  of  the  colour  of  their 
dresses.  The  objects  as  he  apprehended  them  were 
simply  black,  and  nothing  more.  His  intelligence 
rested  in  the  qualitative  total  impression ;  the  vari- 
ous parts,  with  their  quantitative  relations,  which  he 
afterwards  learned  to  know  and  distinguish,  did  not 
at  that  time  exist  for  him. 

It  is  perhaps  impossible  to  find  in  the  experience  of 
an  adult  any  judgments  which  deal  entirely  with  simple 
qualities,  and  which  take  no  account  of  the  numbers,  and 
even  to  some  extent  of  the  relations,  of  the  parts.  But 
we  can  find  examples  of  judgment  where  the  qualitative 
aspect  is  much  the  most  prominent  —  where  indeed  the 
quantitative  and  more  complex  relations  are  scarcely 
noticed  at  all.  '  This  is  green,'  '  that  is  a  strange  odour,' 
'  there  is  something  a  long  way  off,'  — all  these  seem  to 
be  judgments  of  quality  or  general  impression,  and  to 
involve  scarcely  any  other  element.  It  is,  too,  the 
easiest  kind  of  judgment  to  make,  the  judgment  which 
involves  least  mental  effort,  and  which  notices  only 
the  most  evident,  and,  as  it  may  be  seen,  the  most 
superficial,  aspect  of  things.  It  is  evident  that  such 


302  TYPES   OF  JUDGMENT 

judgments  belong  to  a  lower  stage  of  thinking,  than 
those  which  imply  analysis  and  perception  of  quantita- 
tive relations.  Compare,  for  example,  'this  is  very 
large,'  with,  'this  object  is  made  up  of  roots,  trunk, 
branches,  and  leaves ' ;  or  '  this  is  green/  with, '  this  leaf 
is  divided  into  two  parts  by  a  rib  running  through  the 
centre.'  The  first  judgment  in  each  pair  obviously 
involves  much  less  intellectual  work  than  the  latter. 
The  judgment  of  simple  quality  is,  as  we  have  seen,  the 
starting-point  of  thought.  It  is  with  this  kind  of 
thinking  that  the  knowledge  of  the  child  begins.  And, 
before  the  savage  learns  to  count,  i.e.,  to  distinguish 
and  enumerate  the  parts  of  the  objects  with  which  he 
deals,  his  judgments  must  necessarily  belong  to  this 
same  type. 

It  must  never  be  forgotten,  however,  that  simple 
judgments  of  quality  are  really  judgments;  i.e.,  are  not 
given  to  the  mind  from  any  external  source,  but  are  the 
products  of  its  own  activity.  A  judgment,  as  we  have 
already  pointed  out  (§  73),  implies  a  reaction  on  the 
part  of  the  mind  on  what  is  presented  to  consciousness 
through  the  senses.  It  distinguishes  and  puts  together 
the  material  which  sense  presents  in  such  a  way  as  to 
perceive  its  significance  —  what  it  really  amounts  to  — 
as  a  piece  of  knowledge.  This  act  of  interpretative 
intelligence  has  gone,  however,  but  a  little  way  in  the 
type  of  judgment  with  which  we  are  dealing.  But  even 
in  a  vague  qualitative  judgment  like,  'there  is  something 
black,'  the  essential  characteristics  of  Judgment  can  be 
already  distinguished.  For  it  presupposes  at  least  some 
analysis  or  discrimination  of  the  black  object  from  the 


§  82.     JUDGMENTS   OF  QUALITY  303 

rest  of  the  environment,  and  of  the  black  colour  from 
other  colours.  And  the  judgment,  '  something  is  black,' 
has  made  at  the  same  time  a  beginning  in  constructing 
this  vague  something  into  a  system  of  qualities,  or  into  a 
thing  that  is  known.  The  other  qualities  and  relations 
are  as  yet  wrapped  up  in  the  indefiniteness  of  the  'some- 
thing.' In  spite  of  its  indefiniteness,  however,  the  latter 
plays  the  part  of  a  permanent  centre  or  identity.  It  is 
the  whole  from  which  the  quality  of  blackness  has  been 
separated  out,  and  to  which  it  is  again  attached. 

Our  thought,  however,  is  not  satisfied  with  a  know- 
ledge of  the  general  qualities  of  things,  but  pushes 
farther  its  work  of  analysis  and  construction.  In  this 
way,  it  begins  to  distinguish  the  various  parts  of  objects, 
and  to  compare  one  with  another.  We  not  only  judge 
that  '  the  grass  is  green/  but  go  further  and  say  '  this 
piece  is  dark  green,  and  that  light  green.'  The  indefinite 
judgment,  'this  cane  is  heavy,'  is  no  longer  satisfactory, 
and  is  replaced  by,  'this  end  of  the  cane  is  much 
heavier  than  that.'  And  when  this  stage  is  reached, 
judgments  of  Quality  are  already  passing  into  the  next 
higher  type,  judgments  of  Quantity.  For  the  moment 
of  comparison,  which  is  already  contained  in  these 
judgments,  is  the  basis  of  counting,  measuring,  and  all 
quantitative  determination.  In  advancing  from  the 
simple  apprehension  of  quality,  to  take  note  of,  and 
compare,  the  degree  or  intensity  which  the  same  quality 
manifests  in  different  instances,  intelligence  has  entered 
upon  a  path  which  leads  directly  to  judgments  of 
quantity.  To  distinguish  parts,  to  regard  things  as 
degrees  or  instances  of  a  common  quality,  is  at  once 


304  TYPES  OF  JUDGMENT 

to  suggest   the   quantitative   process  of   counting  and 
measurement. 


§  83.  Judgments  of  Quantity.  —  It  is  very  difficult,  as 
we  have  seen,  to  draw  a  hard  and  fast  line  between 
quality  and  quantity.  Indefinite  judgments  of  general 
impression  which  do  not  imply  any  comparison,  seem 
always  to  be  qualitative  rather  than  quantitative  in 
character.  This  is  true,  I  think,  of  judgments  like, 
'this  object  is  very  large,'  'there  was  a  great  flock  of 
sheep  in  the  field.'  In  such  cases,  the  interest  does  not 
seem  to  be  quantitative  at  all ;  i.e.,  there  is  no  effort 
made  to  determine  how  many  units  or  parts  there  are  in 
the  whole  about  which  the  judgment  is  made.  But  the 
general  impression  of  size  or  number  is  apprehended 
and  judged  of  at  the  same  level  of  intelligence,  and  in 
the  same  vague  way,  as  the  simple  qualities  with  which 
we  dealt  in  the  last  section.  It  is  by  means  of  such 
a  general  qualitative  impression  that  the  savage  who 
cannot  count  beyond  five,  is  able  to  distinguish  between 
six  and  some  larger  number.  And  we  must  suppose 
that  the  shepherd's  dog  does  not  learn  that  some  of  the 
sheep  are  missing  by  any  process  of  counting.  We 
must  suppose  that  the  general  qualitative  impression 
made  by  the  smaller  flock  is  different  from  that  made  by 
the  larger,  and  that  there  has  been  no  real  counting  or 
estimation  of  number  in  the  case. 

But  quantitative  judgments  proper  belong  to  a  higher 
stage  of  intelligence  than  do  those  which  have  just 
been  described.  Indefinite  judgments,  like  'this  is  very 
large,'  or,  '  there  are  a  great  many  stars  in  that  group,' 


§  83.     JUDGMENTS   OF  QUANTITY  305 

are  not  satisfactory  pieces  of  knowledge.  We  accord- 
ingly set  ourselves  to  get  more  exact  information  about 
the  parts  which  compose  the  wholes.  The  first  step 
in  this  process  leads  to  Judgments  of  Enumeration.  If 
the  whole  which  is  analyzed  is  composed  of  homogene- 
ous parts,  the  judgments  of  enumeration  take  the  form 
of  simple  counting.  'There  are  one,  two,  three,  .  .  . 
twenty  men  in  this  company.'  Where  the  parts  are 
not  of  the  same  kind,  however,  a  separate  name  may 
have  to  be  given  to  each.  '  This  plant  is  composed  of 
root,  stalk,  leaves,  and  flower.' 

But  exact  quantitative  knowledge  requires  us  to  do 
more  than  enumerate  the  parts  of  which  a  whole  is 
composed.  We  must  go  on  and  weigh  or  measure 
them.  There  is  of  course  no  essential  difference  be- 
tween weighing  and  measuring,  so  that  we  may  call 
all  judgments  which  express  the  result  of  this  process 
Judgments  of  Measure.  It  is  worth  noting  that  judg- 
ments of  this  class  are  not  so  simple  and  direct  as  may 
appear  at  first  sight.  When  we  measure,  we  express 
the  relation  of  the  parts  with  which  we  are  dealing  to 
some  common  unit  or  standard.  The  judgment,  'this 
tower  is  200  feet  high,'  means  that  if  the  tower  is  com- 
pared with  a  foot-rule,  it  will  be  found  to  contain  it 
200  times.  It  really,  then,  involves  a  proportion,  and 
might  be  expressed  :-  tower  :  foot-rule  =  200  :  I. 

The  point  which  it  is  important  to  notice  is  that  all 
measurement  is  the  result  of  comparison.  In  the  first 
place,  some  unit  is  more  or  less  arbitrarily  selected. 
Then  the  judgment  states  simply  the  relation  between 
this  unit  and  the  object  measured :  one  is  contained  in 


306  TYPES   OF  JUDGMENT 

the  other  once,  or  twice,  or  ten  times.  The  quantita- 
tive determination  thus  obtained,  then,  is  merely  rela- 
t^ve.  That  is,  it  does  not  belong  absolutely,  and  in  its 
own  right  to  the  object  measured,  but  indicates  the 
relation  of  that  object  to  something  else. 

For  this  reason,  it  may  seem  that  quantitative  rela- 
tions tell  us  nothing  regarding  the  real  nature  of 
objects,  and  that  to  discover  what  the  latter  are  in 
themselves,  we  shall  have  to  return  to  the  point  of  view 
of  quality.  But  we  have  seen  that  simple  judgments  of 
quality  yield  a  very  unsatisfactory  kind  of  knowledge. 
Moreover,  we  should  find  on  examination  that  even 
qualities  always  imply  a  reference  to  each  other,  and 
are  no  more  absolute  than  quantities. 

In  order  to  obtain  more  satisfactory  knowledge  re- 
garding things,  we  shall  have  to  go  forward  to  a  higher 
type  of  judgment,  rather  than  backward  to  quality. 
But  the  importance  of  quantitative  determination  for 
exact  knowledge  must  not  be  overlooked.  By  means 
of  measurement,  things  are  reduced  to  common  terms, 
as  it  were,  and  thus  a  basis  of  comparison  is  afforded 
where  it  would  otherwise  be  impossible.  To  reduce 
everything  to  such  a  common  measure  is  the  business 
of  the  physico-mathematical  sciences.  Everything  has 
a  quantitative  value,  and  can  be  expressed  mathemati- 
cally in  terms  of  some  unit  or  standard,  as,  for  exam- 
ple, the  unit  of  heat,  or  of  pressure,  or  the  electrical 
unit.  It  was  this  tendency  to  count  and  measure  and 
weigh  things  which  established  the  body  of  exact  know- 
ledge which  we  call  science.  And  in  almost  every  field, 
knowledge  increases  greatly,  both  in  extent  and  exact- 


§  84.     JUDGMENTS   OF  CAUSAL  CONNECTION         307 

ness,  as  soon  as  it  is  found  possible  to  reduce  all  phe- 
nomena to  a  common  measure,  and  to  express  their 
relations  by  means  of  mathematical  formulas. 

It  is  a  great  step  in  advance  to  be  able  to  compare  things  as 
quantities,  and  to  express  their  relations  in  terms  of  number.  But 
judgments  of  quantity  are  not  entirely  satisfactory ;  they  are,  as  has 
already  been  noticed,  merely  relative  in  character.  Moreover,  from 
a  quantitative  point  of  view,  each  thing  is  equivalent  to  the  sum  of 
its  parts.  When  the  parts  have  been  enumerated  and  measured, 
the  value  of  the  whole  is  obtained  by  addition.  But  it  is  scarcely 
ever  possible  to  represent  adequately  the  nature  of  a  whole  in  this 
way.  So  long  as  we  are  dealing  with  a  piece  of  inorganic  matter, 
the  method  of  regarding  the  sum  of  the  parts  as  equivalent  to  the 
thing,  generally  gives  good  results  and  leads  to  no  difficulty.  But  it 
is  quite  different  when  the  whole  in  question  belongs  to  something 
which  has  life  and  consciousness.  In  such  cases,  we  have  what  has 
already  been  called  an  organic  whole  (§  78).  Now,  it  is  clear  that 
the  principle  of  quantity,  which  can  only  add  and  subtract,  is  in- 
sufficient to  represent  completely  the  nature  of  an  object  of  this  kind. 
It  has  no  means  of  representing  the  individuality  or  real  whole, 
which  rather  constitutes  the  parts,  than  is  constituted  by  them. 
That  is,  to  understand  such  objects,  we  shall  have  to  take  a  new 
point  of  view,  and  begin  with  the  whole  rather  than  with  the  parts. 
From  the  point  of  view  of  quantity,  the  nature  of  the  whole  is  dis- 
covered by  adding  together  the  parts  ;  while  in  order  to  understand 
objects  which  possess  an  individuality  of  their  own,  there  seems  to 
be  a  central  principle  to  which  the  parts  are  subordinated,  and  in 
relation  to  which  alone  they  can  be  understood.  The  type  of  judg- 
ments which  deal  with  such  objects  we  shall  have  to  discuss  in 
§85- 

§  84.  Judgments  of  Causal  Connection.  —  Another  class 
of  judgments  used  in  building  up  knowledge,  may  be 
called  judgments  of  Causal  Connection.  They  under- 
take to  show  how  the  various  changes  which  go  on  in 


308  TYPES   OF  JUDGMENT 

things  are  connected  causally  with  other  things  or 
events.  This  type  of  judgment — leading  as  it  does 
beyond  the  particular  object,  to  a  knowledge  of  the  ways 
in  which  objects  are  connected  —  seems  to  belong  to  a 
higher  stage  of  mental  development  than  those  which 
merely  take  note  of  quality  and  quantity.  This  does 
not  mean  that  we  never  look  for  causes,  until  the  quali- 
ties and  quantities  of  things  have  been  discovered.  Nor 
is  it  true  that  any  causal  judgment,  however  vague  and 
unsatisfactory,  is  higher  than  any  judgment  of  quality 
or  quantity  whatsoever.  But,  in  the  beginnings  of  know- 
ledge, one  may  say,  thought  does  not  travel  outside  the 
particular  object  to  show  the  connections  of  the  latter 
with  anything  else.  And  beginning  in  this  way,  it 
seizes  first  upon  quality  and  quantity  which  seem  to  be- 
long to  things  in  themselves.  We  have  seen,  however, 
that  as  a  matter  of  fact  judgments  of  quantity  involve 
comparison,  and  so  a  reference  of  one  thing  to  another, 
though  that  reference  is  not  usually  made  consciously 
or  explicitly.  But,  when  we  judge  that  one  thing  is 
causally  connected  with  another,  the  external  reference 
has  become  explicit,  and  is  the  very  essence  of  the  judg- 
ment. 

The  word  'cause'  has  been  used  in  a  great  many 
senses,  and  its  various  meanings  have  given  rise  to  a 
great  deal  of  discussion.  That  every  event  must  have 
a  cause,  was  formerly  regarded  as  an  innate  truth,  or  a 
priori  proposition.  We  have  seen,  however,  that  we  do 
not  come  into  the  world  with  any  ready-made  stock  of 
knowledge.  All  knowledge,  we  have  often  repeated,  is 
the  result  of  the  mind's  own  judging  activity.  The  so- 


§  84.     JUDGMENTS   OF  CAUSAL  CONNECTION         309 

called  law  of  causation  (every  event  must  have  a  cause) 
must  therefore  express  the  fact  that  thought  does  con- 
nect things  as  causes  and  effects.  Intelligence  is  not 
satisfied  to  take  things  in  isolation  ;  it  tries  to  gain  an 
insight  into  the  ways  in  which  they  are  connected,  to 
discover  what  one  has  to  do  with  another.  And  this  is 
just  the  characteristic  of  thought  which  was  emphasized 
in  §  78.  Judgment,  it  was  there  said,  is  a  process  of 
constructing  a  system,  of  showing  how  the  various  parts 
of  knowledge  fit  into  one  another,  and  are  mutually  de- 
pendent upon  one  another.  The  tendency  of  thought 
to  connect  things  causally,  then,  is  the  same  as  its  ten- 
dency towards  a  system,  which  has  now  become  more 
explicit  and  conscious  of  itself  in  this  type  of  judgment 
than  it  was  in  quality  and  quantity. 

It  will  be  interesting  to  note  some  of  the  most  impor- 
tant changes  which  take  place  in  the  principle  of  causal 
explanation  at  different  stages  in  the  development  of 
knowledge.  The  child  and  the  savage  regard  all 
changes  and  events  which  take  place  in  the  natural 
world,  as  due  to  the  agency  of  living  beings.  These 
beings  are  represented  as  more  or  less  similar  to  men, 
and  as  endowed  with  human  passions  and  emotions. 
Thus  we  say  that  the  earliest  kind  of  explanation  is  es- 
sentially anthropomorphic.  This  word  is  derived  from 
avOpcoTros,  a  man,  and  pop^rf,  shape  or  form,  and  hence 
is  used  to  describe  the  way  of  representing  either  a 
spiritual  being,  as  for  example,  the  Deity,  or  natural 
forces  like  fire,  wind,  etc.,  in  human  form.  It  is  proba- 
bly true  that  at  a  very  early  stage  in  the  development 
of  both  the  individual  and  the  race,  every  object  is 


310  TYPES  OF  JUDGMENT 

supposed  to  have  life.  Or,  perhaps,  it  would  be  truer- to 
say  that  the  young  child  (and  the  same  would  be  true 
for  the  savage  on  a  low  plane  of  intelligence)  has  not 
yet  made  the  distinction  between  animate  and  inani- 
mate objects,  but  vaguely  regards  everything  as  like 
himself.  This  stage  is  usually  known  as  animism, 
because  each  object  is  supposed  to  be  endowed  with 
a  spirit,  or  anima. 

Gradually,  however,  the  distinction  between  animate 
and  inanimate  objects  becomes  clear.  Accordingly, 
we  find  that  at  a  somewhat  more  advanced  stage  the 
mode  of  explanation  takes  a  different  form,  though 
it  is  still  anthropomorphic.  Physical  objects  are  no 
longer  regarded  as  living,  but  the  changes  in  them 
are  supposed  to  be  due  to  the  action  of  spirits,  who 
are  outside  of  the  objects,  but  who  use  them  to  ac- 
complish their  purposes.  These  invisible  spiritual 
agents,  to  whom  all  natural  events  are  referred,  have 
been  variously  named.  It  is  clear,  however,  that  the 
gods  of  mythology  belong  here,  as  well  as  the  fairies, 
elfs,  ghosts,  and  witches  of  the  popular  folk  stories. 
It  was  a  great  advance  when  a  Greek  thinker,  named 
Thales,  came  to  the  conclusion  that  it  does  not  in 
any  way  explain  natural  events  to  refer  them  to  the 
action  of  the  gods.  For,  in  the  first  place,  to  say  that 
the  gods  cause  this  or  that  event,  is  to  state  some- 
thing which  we  have  no  means  of  proving.  And  even 
if  the  assertion  were  true,  it  would  not  really  explain 
anything.  For  it  would  not  enable  us  to  understand 
how  the  changes  in  question  came  about.  It  would 
tell  nothing  whatever  regarding  the  actual  steps  in  the 


§  84.     JUDGMENTS  OF  CAUSAL  CONNECTION         3 1 1 

process  itself.  Thales  saw  this,  and  tried  to  give  a 
natural  explanation  of  the  world,  and  all  that  goes  on 
in  it.  He  tried  to  build  up  a  real  system  of  know- 
ledge by  attempting  to  show  how  everything  which  has 
happened  in  the  world  has  been  connected  with  some 
natural  cause.  We  know  very  little  about  the  actual 
explanation  of  the  world  which  Thales  gave,  except  that 
he  tried  to  derive  everything  from  water.  It  is  on  ac- 
count of  the  method  which  he  adopted,  rather  than  of 
what  he  actually  performed,  that  he  is  regarded  as  the 
founder  of  science.  Thales  first  showed,  one  may  say, 
that  knowledge  means  an  insight  into  the  ways  in  which 
the  actual  phenomena  of  the  world  are  connected.  We 
cannot  unite  into  a  system  things  so  different  in  kind 
as  spirits  and  natural  phenomena.  Or  we  may  say  that 
real  explanation  demands  that  there  shall  be  some  like- 
ness, or  ground  of  similarity,  between  the  cause  and  the 
effect.  An  event  which  happens  in  the  world  of  objects, 
must  be  explained  by  showing  its  connection  with  some 
other  event,  of  a  similar  character,  which  precedes  it. 

The  development  of  this  conception  of  scientific  ex- 
planation also  influenced  still  further  the  notion  of 
causality.  We  have  seen  that  in  the  beginnings  of 
knowledge  every  event  was  supposed  to  be  due  to  the 
action  of  some  living  agent,  or  spiritual  being.  Even 
after  this  mythological  mode  of  explanation  is  dis- 
carded, and  natural  causes  put  in  the  place  of  spirits, 
it  is  still  difficult  to  rid  oneself  entirely  of  the  old  an- 
'thropomorphism.  The  popular  mind  still  tends  to.' 
regard  the  cause  as  an  agent  which  produces  the  effect, 
through  some  power  or  efficiency  which  it  possesses.  It 


312  TYPES   OF  JUDGMENT 

is  not  necessary  to  raise  the  question  at  present  whether 
there  are  any  grounds  for  this  belief.  To  discuss  this 
problem  would  carry  us  beyond  logic  into  metaphysics. 
What  we  wish  to  notice  is  that  science  has  gradually 
abandoned  the  notion  that  the  cause  does  something  to 
the  effect.  That,  as  we  have  seen,  is  a  remnant  of  the 
old  prescientific  idea,  and  a  notion  which  does  not  aid 
at  all  in  explaining  our  knowledge.  It  is  the  business 
of  science  to  show  how  the  things  and  events  which 
make  up  our  experience  are  necessarily  connected  with 
one  another.  Science  has  to  discover  what  things  in- 
variably go  along  with  one  another,  and  necessarily  pre- 
suppose one  another.  And,  when  it  is  found  that  some 
particular  thing  or  event,  A,  invariably  precedes  another 
particular  occurrence,  B,  the  former  is  regarded  as  the 
cause,  and  the  latter  as  the  effect.  In  order  to  elimi- 
nate as  far  as  possible  the  notion  of  agency  or  effi- 
ciency which  attaches  to  the  word  cause,  the  terms 
'  antecedent '  and  '  consequent '  are  often  used  to  in- 
dicate this  relation.  For  science,  the  cause  is  not  an 
active  agent,  but  the  invariable  antecedent  of  something 
else  which  simply  follows  it.  The  cause  does  not  explain 
the  effect  by  assigning  an  agent  which  brings  the  latter 
about  through  its  personal  efforts ;  but  it  explains, 
because  it  reveals  another  necessary  step  in  the  process, 
and  gives  us  a  new  fact  which  joins  on  or  can  be  con- 
nected with  the  one  from  which  we  start. 

We  conclude  then  that  the  cause  of  any  event  is  its 
invariable  and  necessary  antecedent.  In  another  part  of 
this  book  (Chs.  XV.,  XVI.),  it  is  shown  what  tests  it  is 
necessary  to  apply  in  order  to  determine  whether  two 


§  84.     JUDGMENTS   OF  CAUSAL  CONNECTION         3 1 3 

phenomena  are  merely  accidentally  conjoined,  or  whether 
the  connection  is  essential  and  real.  It  is  necessary  now 
to  take  one  more  step  in  tracing  the  various  ways  in 
which  the  idea  of  causality  has  been  used.  As  a  re- 
sult of  a  famous  scientific  discovery,  which  was  made 
about  the  middle  of  the  present  century,  a  new*  element 
has  been  added  to  the  notion  of  cause  in  its  application 
to  physical  phenomena.  The  law  of  the  Conservation 
of  Energy  states  that  the  amount  of  energy,  or  power  of 
doing  work,  possessed  by  any  set  of  bodies,  remains  con- 
stant. Any  change  in  a  material  body  is  the  result  of 
a  transformation  of  energy  from  one  form  to  another. 
The  same  is  true  of  the  world  as  a  whole :  the  total 
amount  of  energy  which  it  contains  remains  constant. 
All  changes  which  take  place  in  the  physical  universe 
—  motion  into  heat,  or  electricity  into  motion  —  are  sim- 
ply different  forms,  or  manifestations,  of  the  one  world- 
energy. 

As  a  result  of  this  law,  the  effect  always  represents 
the  same  amount  of  energy,  or  power  of  doing  work, 
as  the  cause.  Since  no  energy  is  ever  lost,  the  one 
must  be  equal  to  the  other.  And,  as  a  matter  of  fact, 
the  quantitative  equivalence  of  many  of  the  various  forms 
of  energy  has  been  proved  by  actual  measurement.  In 
working  out  this  law,  for  example,  Joule  showed  that 
"the  energy  stored  up  in  the  I  Ib.  weight  which  had  been 
pulled  up  772  feet  was  gradually  transformed,  as  soon  as 
the  weight  was  released,  into  an  amount  of  heat  capable 
of  raising  the  temperature  of  a  pound  of  water  i° 
Fahr. ;  while  Him  showed,  on  the  other  hand,  that  ex- 
actly this  amount  of  heat  would,  if  it  could  be  turned 


314  TYPES   OF  JUDGMENT 

back   again  into  energy,  raise  the   i  Ib.  weight  to  the 
height  of  772  feet  at  which  it  stood  before."  l 

The  new  element  which  this  law  adds  to  the  idea  of 
cause  as  a  necessary  and  invariable  antecedent,  is  that  of 
the  quantitative  identity  of  cause  and  effect.  Taking  the 
phenomena  which  are  connected  in  this  way  to  repre- 
sent simply  certain  quantities  of  energy,  we  say  that  the 
one  is  equivalent  to  the  other.  The  energy  which  the 
cause  represents  has  been  transformed  without  loss,  and 
reappears  in  the  effect.  If  what  seems  to  be  the  total 
effect  is  not  equal  to  the  cause,  part  of  the  energy  of 
the  latter  must  have  been  transformed  into  something 
else.  No  energy  can  have  been  lost. 

It  becomes,  therefore,  the  task  of  the  physical  sci- 
ences to  show  that  this  relation  of  quantitative  identity 
exists  between  phenomena  which  are  causally  connected. 
The  ideal  of  physical  science,  is  to  prove  that  two  phe 
nomena  are  connected  as  cause  and  effect,  by  showing' 
that  both  represent  the  same  quantity  of  energy.  For 
this  purpose,  measurement  and  calculation  are  neces- 
sary. The  physical  sciences,  as  was  pointed  out  in  the 
last  section,  deal  largely  with  judgments  of  quantity, 
and  devote  themselves  to  showing  by  measurement  that 
the  same  amount  of  energy  persists  through  the  various 
changes  which  phenomena  undergo.  In  establishing 
causal  connections,  the  physical  sciences  find  it  necessary 
to  use  the  principles  .of  measurement  and  calculation. 

It  will  be  evident,  from  what  has  been  already  stated,  that  this 
relation  of  cause  and  effect  should  apply  to  all  phenomena  whose 

1  Buckley,  Short  History  of  Natural  Science,  p.  339. 


§85.    JUDGMENTS  OF  INDIVIDUALITY  315 

energy  is  capable  of  being  measured  and  represented  in  quantitative 
terms.  As  a  matter  of  fact,  however,  the  law  has  been  proved  only 
in  physics  and  chemistry.  From  the  very  nature  of  the  case,  it  is 
extremely  difficult  to  measure  exactly  the  relations  of  cause  and  effect 
in  the  sciences  which  deal  with  organic  life.  But  even  in  those 
sciences,  the  law  of  the  Conservation  of  Energy  is  assumed  to  hold 
true.  For  example,  the  amount  of  energy  which  a  plant  contains,  is 
assumed  to  be  exactly  the  same  as  that  represented  by  the  various 
elements  or  forces  —  water,  sunlight,  mineral  substances,  etc.  — 
which  were  instrumental  in  composing  it.  In  the  same  way,  we 
suppose  that  the  same  relation  holds  of  the  changes  which  go  on 
in  the  brain,  though  we  are,  of  course,  unable  to  prove  this  by 
actual  measurement. 

It  is  difficult,  however,  to  see  how  this  law  can  have  any  applica- 
tion to  mental  phenomena.  We  can  indeed  measure  the  intensity 
and  duration  of  sensations.  But  neither  feelings  nor  complex  pro- 
cesses of  mind  seem  to  be  capable  of  measurement.  Moreover,  it  is 
never  possible  to  measure  the  energy,  or  power  of  doing  work,  which 
states  of  consciousness  possess,  and  to  equate  one  with  another  in 
this  respect.  And  this  being  so,  the  law  of  the  Conservation  of 
Energy  cannot,  of  course,  apply  to  psychical  causes  and  effects.  In 
the  mental  sciences,  then,  we  cannot  claim  that  the  notion  of  Cau- 
sality contains  the  element  of  quantitative  identity  between  cause 
and  effect  which  has  been  found  to  exist  in  the  physical  sciences.1 

§  85.  Judgments  of  Individuality.  —  By  Judgments  of 
Individuality,  we  mean  judgments  which  regard  some 
complex  object  as  a  real  whole  with  a  definite  nature  of 
its  own.  We  have  already  had  occasion  (§  78)  to  dis- 
tinguish a  mere  aggregate  or  sum  of  parts,  like  a  heap 
of  stones,  from  a  true  whole  which  possesses  a  certain 
character  and  individuality  of  its  own.  It  is  the  former 
point  of  view  from  which  judgments  of  quantity  and 

1  Cf.  Wundt,  Ethik  (ist  ed.)  pp.  398  f.;   Sigwart,  Logic,  §  97  a,  7. 


3l6  TYPES  OF  JUDGMENT 

of  causal  connection  regard  objects.  For  these  types  ot 
judgments  are  concerned  wholly  with  the  parts  —  the 
former  to  measure,  and  the  latter  to  show  their  causal 
connection.  It  requires  a  new  form  of  judgment  to 
represent  adequately  the  nature  of  a  complex  object 
which  possesses  individuality.  This  form  gives  expres- 
sion to  the  organic  unity  and  wholeness  of  things,  and 
emphasizes  the  way  in  which  the  parts  cooperate  for  a 
common  purpose  or  end.  Thus  we  regard  the  parts  of 
a  plant  as  a  unity  cooperating  in  a  common  purpose, 
and  a  man  as  a  conscious  system  of  ends. 

(i)  We  have  seen  that  judgments  of  causal  connection  relate  phe- 
nomena as  causes  and  effects.  A  change  in  an  object  is  explained 
by  showing  that  some  other  change  or  event  invariably  precedes  it. 
But  this  change,  in  its  turn,  demands  explanation,  and  has  to  be 
accounted  for  by  the  discovery  of  a  new  cause.  This  type  of  judg- 
ment shows  that  one  phenomenon  is  connected  with  a  second,  and 
a  second  with  a  third,  and  so  on  indefinitely.  The  view  of  the 
world  which  it  presents  is  that  of  a  never-ending  series  of  causes 
and  effects.  It  is  never  possible  to  find  a  cause  which  is  not  itself 
the  effect  of  something  else.  No  phenomenon  possesses  any  inde- 
pendence of  its  own,  but  is  simply  a  link  in  a  series,  or  a  piece  of 
a  whole  that  is  never  completed. 

In  the  last  section,  it  was  stated  that  causal  judgments  connect 
one  part  of  our  knowledge  with  another,  and,  in  this  way,  aid  in 
uniting  the  parts  of  our  experience  in  a  systematic  way.  Now  it 
is  undoubtedly  true  that  it  would  be  impossible  to  have  any  real 
knowledge  of  anything  as  a  whole,  or  an  individual,  without  know- 
ing the  way  in  which  the  parts  are  related,  and  mutually  depend 
upon  each  other.  In  that  sense,  judgments  of  causal  relation  are 
indispensable  to  a  knowledge  of  a  true  whole.  But  this  form  of 
judgment  itself  resolutely  goes  on  connecting  part  with  part  —  one 
phenomenon  with  another  —  and  refuses  to  regard  any  group  of 
parts  as  possessed  of  an  independent  character  or  individuality 


§85.    JUDGMENTS  OF  INDIVIDUALITY  317 

From  this  point  of  view,  everything  is  externally  determined ;  its 
cause,  or  principle  of  explanation,  lies  outside  of  it  in  something 
else.  The  mark  of  individuality,  on  the  other  hand,  is  the  power 
of  origination,  or  self-determination. 

(2)  Psychology,  one  may  say,  adopts  the  standpoint  of  Causal 
Connection ;  Ethics,  that  of  Individuality.  The  former  science  re- 
gards mind  as  a  sum  of  mental  processes,  and  undertakes  to  show 
how  its  various  parts  are  connected.  Every  state  of  consciousness 
is  supposed  to  be  determined  by  something  external  to  itself — some 
antecedent  mental  state,  or  some  bodily  process.  The  interest,  as 
was  previously  said,  is  centred  in  the  parts,  and  it  is  very  rarely  that 
the  psychologist  stops  to  look  at  the  mind  as  a  whole.  Ethics,  on 
the  other  hand,  has  to  begin  with  the  individual.  It  does  not  regard 
mind  as  a  thing  or  substance  (that  is  the  naive  point  of  view  against 
which  psychology  rightly  warns  us),  but  as  a  self-conscious  system 
of  ideas,  purposes,  and  feelings,  which  possesses  the  power  of  initia- 
ting action,  and  of  determining  itself.  Ethics  can  adopt  all  that  psy- 
chology has  to  tell  regarding  the  mechanism  of  the  mental  processes. 
Indeed,  without  a  systematic  and  detailed  account  of  the  nature  and 
laws  of  mental  life  it  could  have  no  adequate  conception  of  mind 
as  a  whole :  the  judgment  of  Individuality  must  use  the  results  of 
judgments  of  Causal  Connection.  What  it  really  does,  is  to  trans- 
form the  sum  of  mental  processes  into  a  system  which  has  a  real 
unity  of  its  own.  For  it  is  only  when  a  person  is  regarded  as  a 
self-conscious  and  self-acting  individual,  that  he  can  be  supposed 
capable  of  conduct  to  which  the  terms  '  moral '  and  i  immoral '  can 
properly  be  applied. 

References 

Hegel,  Logic,  Pt.  II.,  The  Doctrine  of  Essence  (Wallace's  trans., 
2d  ed.),  pp.  206-286. 

B.  Bosanquet,  Logic,  Vol.  I.  Chs.  II. -V. 
J.  S.  Mill,  Logic,  Bk.  III.  Ch.  V. 

C.  Sigwart,  Logic,  §  73. 


CHAPTER    XXIV 

THE     NATURE    OF     INFERENCE.  INDUCTION     AND 

DEDUCTION 

§  86.  Judgment  and  Inference.  —  It  must  not  be  for- 
gotten  that  our  object  in  these  chapters  is  to  obtain  as 
definite  a  conception  as  possible  regarding  the  nature  of 
thought.  To  attain  this  end,  we  agreed  (§  73)  that 
it  would  be  advantageous  to  begin  with  the  simplest  or 
most  elementary  form  of  thinking.  That  form  we  found 
to  be  Judgment.  We  have  now  endeavoured  to  show 
what  Judgment  is,  and  what  part  it  plays  in  building  up 
knowledge.  And,  in  the  last  chapter,  we  have  attempted 
to  see  some  of  the  steps  in  the  evolution  of  Judgment, 
as  it  passes  from  simple  judgments  of  Quality  to  judg- 
ments of  Individuality.  This  account  being  completed, 
it  remains  now  to  discuss  the  nature  of  reasoning  or 
Inference. 

We  shall  probably  get  the  clearest  idea  of  the  nature 
of  Inference  by  regarding  it  as  a  completely  developed 
judgment.  As  thinking  develops  from  the  form  of  sim- 
ple judgment  to  that  of  Inference,  it  displays  progressive 
differentiation  and  integration.  In  accordance  with  this 
law,  we  can  say  (i)that  Inference  is  more  complex  than 
Judgment.  The  latter  process,  in  its  simplest  form,  can 
scarcely  be  said  to  have  any  parts  :  it  represents  a  single 
act  or  pulsation  of  intelligence.  Inference,  on  the  other 

318 


§86.     JUDGMENT  AND   INFERENCE  319 

hand,  seems  to  imply  steps  or  stages  in  thinking  —  a 
passage  of  the  mind  from  one  fact  to  another.  More- 
over, (2)  Inference  differs  from  Judgment  in  exhibiting 
the  grounds  upon  which  its  statement  rests.  The  sim- 
ple judgment  makes  a  declaration  on  the  basis  of  sense- 
perception,  as,  for  example,  'the  mail-train  has  just  gone 
down ' ;  '  it  rained  yesterday.'  Each  of  these  statements 
stands  alone,  as  it  were ;  it  does  not  attempt  to  gain 
support  by  pointing  out  the  connection  with  other  facts. 
To  infer,  however,  is  just  to  show  the  necessary  con- 
nection of  facts  —  that  from  the  presence  or  absence 
of  certain  things,  the  presence  or  absence  of  certain 
other  things  necessarily  follows.  It  is  not  necessary 
for  Inference  that  the  conclusion  reached  should  be  a 
fact  which  was  not  hitherto  known.  We  often  do  reach 
new  truths  by  reasoning  from  necessary  connections. 
Thus  we  might  infer  that  the  mail-train  has  just  gone 
down,  from  the  fact  that  this  train  is  always  on  time, 
and  that  it  is  now  five  minutes  past  the  hour.  Or,  we 
might  prove,  to  a  person  who  doubted  the  correctness  of 
our  memory,  that  it  rained  yesterday,  by  pointing  to 
other  facts  with  which  rain  is  necessarily  connected. 
We  might  point  to  the  muddy  condition  of  the  roads, 
the  swollen  streams,  or,  perhaps,  might  remind  the  per- 
son who  questions  the  statement,  that  it  was  yesterday 
that  A  was  out  driving,  and  came  home  soaking.  In 
this  way,  one  tries  to  exhibit  the  necessity  of  the  fact 
under  consideration ;  and  to  do  this  is  to  infer. 

In  the  actual  process  of  knowledge,  we  more  fre- 
quently go  from  a  fact  to  its  reasons,  than  in  the  oppo- 
site direction.  The  intelligence  begins  by  accepting  all 


320  THE  NATURE  OF   INFERENCE 

the  connections  as  true  and  universal  which  it  meets 
with  in  ordinary  experience,  or  which  are  suggested  to 
it  in  any  way.  It  does  not  trouble  itself  at  all  about 
the  grounds  of  its  judgments,  and  thus  the  insufficient 
basis  on  which  many  of  these  stand  is  at  first  not  evi- 
dent. The  child,  for  example,  believes  everything  which 
it  is  told  by  its  mother  or  nurse,  or  it  may  be,  all  the 
pleasant  things  which  it  imagines.  Very  often,  too,  the 
judgments  of  older  persons  are  determined  by  their  own 
wishes.  The  French  peasant  girl  was  sure  that  it  was 
impossible  for  the  Germans  to  take  Paris.  Another 
principle  upon  which  both  children  and  adults  quite 
unconsciously  proceed,  is  that  the  future  must  always 
resemble  the  past.  The  child  assumes  that  the  order 
of  events  each  day  will  be  the  same,  —  that  there  will 
always  be  games  after  dinner,  and  visitors  in  the  after- 
noon, because  that  has  happened  a  number  of  times  in 
the  past.  And  one  may  have  no  better  reason  for 
believing  that  the  sun  will  rise  to-morrow,  than  the  fact 
that  it  rose  yesterday  and  to-day. 

In  these  early,  unreflective  judgments,  the  ground  or 
principle  upon  which  they  are  based  is,  of  course,  not 
conscious  at  all.  Each  judgment  is  accepted  by  itself, 
and  no  questions  are  raised  as  to  how  it  is  known.  But 
the  development  of  intelligence  may  be  regarded  as  a 
process  of  becoming  conscious  of  the  reasons  which 
show  the  falsity  of  certain  of  our  beliefs,  and  the  neces- 
sity of  others.  The  original  judgment  is  not  in  reality 
so  isolated  and  unrelated  as  it  appeared ;  it  contains 
implicitly  its  own  reasons.  But  the  validity  of  its  pro- 
cedure cannot  be  made  manifest,  until  the  reasons 


§86.    JUDGMENT   AND   INFERENCE  32! 

for  the  statement  made  by  the  judgment  are  brought 
to  light.  In  the  development  of  knowledge,  the  judg- 
ment must  expand  so  as  to  show  the  reasons  which  it 
necessarily  presupposes.  In  itself,  it  is  only  a  fragment 
of  the  complete  statement,  and  it  tries  to  complete  itself 
by  making  clear  the  nature  of  the  whole  which  it  in- 
volves. It  is  not  until  the  implicit  reasons  which  every 
judgment  contains  are  thus  brought  to  consciousness, 
that  it  can  be  either  proved  or  disproved.  Taking  the 
mere  judgment  by  itself,  it  is  only  possible  to  place 
one  man's  assertion  against  another's  denial.  But  proof 
or  disproof  of  a  proposition  implies  that  reasons  are 
given  for  or  against  it.  If  its  connection  with  some 
fact,  or  set  of  facts,  known  to  be  true,  becomes  evident 
on  reflection,  the  felt  necessity  which  the  judgment 
possesses  (§  76),  is  transformed  into  logical  necessity. 
But,  if  no  such  connection  can  be  found,  or,  if  the 
judgment  in  question  is  seen  to  presuppose  propositions 
which  are  themselves  false,  we  must,  of  course,  cease  to 
regard  it  as  valid. 

When  a  judgment  develops  so  as  to  become  conscious  of  its 
reasons,  it  has  already  taken  on  the  form  of  Inference.  And,  as 
we  have  already  seen,  this  is  the  usual  procedure  of  knowledge. 
We  begin  by  believing  without  reason,  or  we  assume  that  certain 
things  are  true,  and  try  to  find  reasons  for  our  belief.  The  conclu- 
sion, which  is,  of  course,  logically  last,  is  usually  first  for  us,  and  we 
set  out  from  it  to  find  the  grounds,  or  the  premises. 

This  way,  however,  of  proceeding  from  conclusion  to 
premises,  or  from  a  judgment  to  its  reasons,  implies 
that  the  mind  is  already  aware  of  the  distinction  be- 
tween false  knowledge  and  true,  and  therefore  that  the 


322  THE  NATURE  OF  INFERENCE 

work  of  criticising  and  testing  knowledge  has  already 
begun.  The  criticism  of  knowledge  is  probably  forced 
upon  the  mind  at  first  by  the  practical  consequences  of 
false  judgments.  So  long  as  false  judgments  lead  to 
no  unpleasant  results,  they  are  likely  to  pass  unnoticed, 
without  any  question  being  raised  regarding  the  grounds 
by  means  of  which  they  are  supported.  The  child  usu- 
ally believes  all  that  he  is  told,  until  he  discovers  that 
his  credulity  is  making  him  a  laughing-stock,  or  has  led 
to  the  loss  of  some  pleasure  which  he  values.  Sooner 
or  later  he  learns  that  the  ground  upon  which  he  has 
been  unconsciously  proceeding  —  somebody  told  me  — 
is  insufficient.  In  the  same  way,  the  natural  tendency 
to  regard  all  connections  which  we  happen  to  find  ex- 
isting between  events  as  universal  and  necessary,  be- 
comes more  critical  and  discriminating.  The  child  soon 
learns  that  the  events  of  one  day  do  not  necessarily 
follow  in  the  order  of  the  day  before,  and  that  it  is  not 
always  rainy  on  Fridays,  and  fine  on  Sundays.  But,  in 
order  to  discriminate  between  what  is  true  and  what  is 
false,  he  is  obliged  to  go  beyond  the  facts  themselves, 
and  to  become  more  or  less  clearly  aware  of  the  grounds 
assumed  in  each  type  of  judgment.  He  is  forced  to 
include  in  the  judgment  the  reasons  by  which  it  is  sup- 
ported. And,  in  this  way,  the  distinction  between  valid 
and  invalid  principles  of  connection  is  gradually  learned. 
Through  experience,  which  is  more  or  less  dearly 
bought,  we  learn  that  we  cannot  depend  upon  hear- 
say, and  also  that  many  of  the  most  obvious  connec- 
tions between  events  are  not  essential,  and  have  no 
claim  to  be  regarded  as  universal  laws.  It  becomes 


§  86.     JUDGMENT   AND   INFERENCE  323 

evident  that  it  is  necessary,  in  order  to  reach  true 
principles  of  connection,  to  take  a  wider  survey  of  the 
facts,  and  to  push  the  process  of  analysis  further  than 
is  done  by  our  ordinary  judgments  of  sense-perception. 
For  example,  we  may  at  one  time  have  supposed  it  to 
be  a  universal  law  that  hot  water  will  break  glasses 
when  poured  into  them.  But  as  soon  as  we  have  ex- 
perience of  any  instance  or  instances  to  the  contrary, 
we  see  that  there  is  no  essential  connection  between 
hot  water  and  broken  glasses.  It  is  necessary  then  to 
go  behind  the  obvious  facts  of  the  case,  in  order  to  dis- 
cover what  is  the  real  antecedent  in  the  two  cases. 
The  two  instances  —  where  the  glasses  break,  and  where 
they  do  not  —  seem  to  be  the  same ;  and  yet,  since 
the  result  is  different,  there  must  be  a  difference  which 
further  analysis  will  bring  to  light.  It  is  by  penetrat- 
ing behind  the  point  of  view  of  ordinary  knowledge, 
that  science  endeavours  to  show  how  phenomena  are 
really  and  essentially  connected. 

The  judgments  of  ordinary  adult  life  usually  involve  some  con- 
sciousness of  their  grounds,  and  are  therefore  so  far  inferences. 
But  in  many  cases  of  this  kind  it  would  be  difficult  for  the  individual 
to  state  explicitly  the  reasons  for  his  judgment.  The  connection 
which  he  asserts  may  be  guaranteed  to  his  mind  by  some  complex 
set  of  circumstances  very  difficult  to  formulate.  Or  it  may  rest 
upon  some  general  similarity  or  analogy,  which  is  so  obviously  in- 
sufficient that  he  hesitates  to  acknowledge  that  it  is  the  only  ground 
he  has  for  judging.  Thus  one  may  be  vaguely  conscious  that 
one's  only  reason  for  liking  A  is  his  resemblance  to  B.  It  may  be 
impossible  to  say  exactly  in  what  points  A  resembles  B ;  one  may 
proceed  on  a  vague  general  similarity.  Or  one  may  hesitate  to 
make  clear,  even  to  oneself,  that  the  only  reason  for  disliking  A  is 


324  THE  NATURE  OF  INFERENCE 

because  of  some  external  resemblance  —  in  name,  or  dress,  or  figure 
—  to  C,  whom  one  dislikes. 

§  87.  The  Nature  of  Inference.  —  We  have  seen  that 
it  is  difficult  to  draw  any  hard  and  fast  line  between 
Judgment  and  Inference.  In  general,  however,  we  may 
be  said  to  reason  when  we  do  not  simply  accept  a  fact 
on  the  basis  of  sense-perception  or  memory,  but  show 
that  it  necessarily  follows  from  some  other  known  fact 
or  facts.  Inference,  then,  requires  (i)  that  certain  data 
or  premises  should  be  accepted  as  already  known  ;  and 
(2)  it  implies  an  insight  into  the  necessary  connection 
of  some  new  fact  or  set  of  facts  with  what  we  already 
know.  Thus  one  is  said  to  infer  B,  when  one  sees  that 
it  necessarily  follows  from  some  fact  which  is  already 
known.  It  is  not  necessary  for  an  inference  that  B 
should  never  have  been  in  consciousness  before.  As 
we  have  seen  in  the  last  section,  what  we  very  often  do 
in  inference  is  to  show  the  reasons  or  necessity  of  some 
fact  which  we  have  previously  accepted  without  know- 
ing why.  No  matter  whether  we  go  from  premises  to 
conclusion  (from  the  reasons  to  the  fact),  or  in  the 
opposite  direction,  from  the  conclusion  to  the  premises, 
we  are  said  to  infer  whenever  we  find  the  ground  for 
the  existence  of  one  fact  in  the  nature  of  another  fact. 
In  the  former  case,  we  use  words  like  '  therefore '  and 
*  consequently/  to  indicate  the  connection ;  and  when 
the  reasons  are  stated  last,  '  for '  and  *  because.'  When- 
ever these  conjunctions  are  used  correctly,  an  infer- 
ence has  been  made,  and  it  is  always  useful  in  following 
a  course  of  reasoning  to  make  clear  to  ourselves  pre- 
cisely on  what  grounds  it  has  been  made. 


§  87.    THE  NATURE  OF  INFERENCE  325 

Although  Inference  seems  very  simple  and  very 
natural,  its  procedure  is  much  more  puzzling,  when 
looked  at  closely,  than  one  would  at  first  imagine.  As 
we  have  seen,  there  is  no  Inference  unless  the  result 
reached  is  different  from  the  starting-point.  But  how 
are  we  ever  justified  in  passing  from  a  knowledge  of 
one  fact  to  another  different  from  it  ?  How  can  we 
ever  pass  from  the  known  to  the  unknown  ?  The 
Greeks,  who  loved  to  bring  to  light  the  paradoxes 
which  so  often  underlie  familiar  facts,  used  to  discuss 
this  question.  How  is  it  possible  for  that  which  is 
unknown  —  external  to  the  mind  —  to  pass  into  the 
mind  and  get  itself  known  ?  It  was  to  solve  this  puz- 
zle that  Plato  propounded  the  doctrine  that  all  knowing 
is  remembering.1  Knowledge,  he  declares,  is  not  in- 
creased by  learning  that  of  which  we  were  altogether 
ignorant,  but  by  a  process  of  calling  to  mind  or  recol- 
lecting the  knowledge  which  the  soul  possessed  in  a 
previous  state  of  existence,  but  which  was  forgotten 
when  it  entered  upon  the  conditions  of  the  present  life. 
It  was  therefore  no  longer  necessary  to  suppose,  accord- 
ing to  Plato,  that  the  mind  performed  the  impossible 
feat  of  knowing  what  is  external  to  itself,  or  that  things 
previously  unknown  pass  bodily  into  our  minds,  and 
thus  become  known. 

Plato  was  undoubtedly  right  in  protesting  against  the 
popular  view  that  knowledge  is  received  into  the  mind, 
as  food  is  received  into  the  stomach.  Knowledge, 
as  we  have  frequently  seen,  comes  from  within,  not 

1  This  is  the  theory  upon  which  Wordsworth  bases  his  "  Ode  on  the 
Intimations  of  Immortality." 


326         THE  NATURE  OF  INFERENCE 

from  without.  But  the  apparent  paradox  of  knowledge 
may  be  explained  without  adopting  Plato's  poetical 
notion  of  a  previous  state  of  existence.  We  may  admit 
that  the  process  of  inference  would  be  quite  inex- 
plicable, if  it  proceeded  from  one  fact,  A,  to  a  know- 
ledge of  a  second  fact,  B,  which  is  totally  different  from 
the  former.  When  we  examine  cases  of  inference,  how- 
ever, we  find  that  there  is  always  a  certain  amount  of 
identity  between  the  two  ends  of  the  process.  The  con- 
clusion is  always  different,  and  yet  not  entirely  different 
from  the  premises.  Thus,  from  the  propositions,  'all 
metals  are  elementary  substances/  and  '  gold  is  a  metal,' 
one  can  infer  that  gold  is  an  elementary  substance. 
It  is  possible  to  connect  '  gold '  and  '  elementary.'  Here 
the  identical  link — what  is  called  in  formal  logic  the 
middle  term  —  is  'metal.'  It  is  possible  to  connect  gold 
and  elementary  substance,  because  the  former  is  at  the 
same  time  a  metal,  which  in  its  turn  is  an  element.  Of 
course,  these  conceptions  —  gold,  metal,  element  —  are 
not  absolutely  indentical ;  it  was  pointed  out  in  (§  79) 
that  propositions  cannot  be  regarded  as  expressing 
mere  identity  without  difference.  But  we  can  say  that 
there  is  a  common  thread  or  element  running  through 
these  notions,  which  furnishes  the  principle  of  con- 
nection. Where  we  cannot  discover  such  a  common 
nature,  no  inference  can  be  made.  Thus,  for  example, 
it  would  be  impossible  to  draw  any  conclusion  from 
the  statements  that  '  it  rained  yesterday '  and  '  gold  has 
been  discovered  in  Alaska,'  because  there  is  no  com- 
mon element  or  connecting  thread  present  which  would 
lead  us  beyond  the  premises. 


§  87.  THE  NATURE  OF  INFERENCE        327 

In  formal  arguments  the  middle  term,  or  connecting  link,  is  usu- 
ally explicitly  stated ;  but  in  the  actual  process  of  reasoning  things 
out,  it  is  frequently  necessary  to  go  in  search  of  it.  We  may  notice, 
for  example,  that  the  fire  in  a  stove  burns  more  slowly  when  the 
damper  is  shut.  In  order  to  understand  the  fact,  we  have  to  find  out 
some  fact  which  is  common  to  ( closed-damper '  and  '  slow-burning,' 
some  link  of  identity,  as  it  were,  which  enables  us  to  pass  from  the 
one  to  the  other.  Such  a  connecting  link  is  afforded,  of  course,  in 
this  case  by  the  supply  of  oxygen.  Darwin  was  noted  for  his  keen- 
ness in  detecting  connections  which  escaped  the  ordinary*  eye,  as 
well  as  for  his  skill  in  giving  explanations  of  them.  On  one  occa- 
sion, he  observed  that  in  the  part  of  the  country  where  he  lived, 
clover  was  abundant  in  those  fields  which  were  situated  near  villages, 
while  the  outlying  fields  were  almost  destitute  of  it.  What  now,  he 
asked  himself,  is  the  connecting  link  between  these  facts  ?  Some 
investigation  of  the  matter  convinced  him  that  the  two  agencies 
which  produced  this  result  were  mice  and  cats.  The  field  mice 
destroy  the  clover  by  feeding  upon  its  roots,  but  the  cats  go  out  from 
the  villages  into  the  fields  near  by  and  kill  the  mice. 

We  have  seen  that  the  passage  from  one  fact  to  an- 
other in  inference  does  not  involve  a  transition  to  some- 
thing wholly  different  from  the  starting-point.  There  is 
always  some  aspect  or  feature  in  which  the  premises  are 
identical  with  the  conclusion.  And  it  is  on  the  strength 
of  this  identity  that  a  passage  can  be  made  from  one  to 
the  other.  The  same  fact  may  be  expressed  differently 
by  saying  that  all  inference  takes  place  within  a  system, 
'where  the  parts  are  so  held  together  by  a  common 
nature  that  you  can  judge  from  some  of  them  what  the 
nature  of  the  others  must  be.'  Suppose  you  were  given 
the  leaf  of  a  plant.  If  you  had  some  systematic  botani- 
cal knowledge,  it  would  be  possible  to  infer  the  species 
of  plant  to  which  the  leaf  belonged.  That  is,  from 


328  THE  NATURE  OF  INFERENCE 

the  nature  of  a  part,  the  nature  of  the  whole  to  which  it 
belongs  could  be  determined.  The  part  represents  the 
whole  —  in  some  sense  contains  it  implicity.  It  is  said 
that  the  great  naturalist  Cuvier  could  determine  by  ex- 
amining a  single  tooth  the  nature  of  the  animal  to  which 
it  belonged.  Let  us  suppose  that  the  tooth  were  that  of 
a  ruminant  animal.  Now  a  zoologist,  who  knows  the 
characteristics  of  such  an  animal,  could  draw  various  in- 
ferences regarding  the  possessor  of  the  tooth.  He  could 
conclude,  for  example,  that  the  animal  to  which  it  once 
belonged  must  also  have  had  cloven  hoofs.  A  single 
piece  or  part,  that  is,  would  enable  one  who  knows  the 
system  or  common  nature  to  which  all  the  parts  be- 
long, to  judge  what  the  other  parts  are  like. 

The  examples  just  given  have  referred  to  the  possi- 
bility of  an  inference  from  one  part  of  an  organism  to 
another.  But,  as  we  have  already  seen,  the  systematic 
connection  which  here  exists  between  the  parts,  is  more 
or  less  completely  present  whenever  it  is  possible  to 
infer  at  all.  Inference  pushes  further  the  work  of  con- 
structing a  system  begun  by  Judgment  (§  78).  If  each 
thing  was  known  by  itself,  if  the  parts  of  our  knowledge 
did  not  fall  together  into  systems  where  each  part  to 
some  extent  determines  the  nature  of  the  other  parts,  no 
inference  would  be  possible.  It  is  because  the  various 
pieces  of  our  knowledge  are  never  independent  of  each 
other,  but  form  an  organic  whole,  like  the  members  of  a 
living  organism,  that  certain  facts  follow,  as  we  say, 
from  certain  other  facts.  And  it  is  of  course  true,  that 
as  our  knowledge  in  any  field  becomes  more  completely 
organized,  it  is  more  possible  to  use  it  as  a  basis  for  in- 


§  88.     INDUCTION  AND   DEDUCTION  329 

ference.  The  better  we, are  able  to  put  together  in  a 
systematic  way  the  various  facts  which  we  have  learned 
about  geology,  or  astronomy,  or  the  weather,  the  more 
significant  each  fact  becomes.  The  geologist  may  be 
able  to  tell  from  the  appearance  of  the  cliffs  what  has 
taken  place  in  a  locality  thousands  of  years  ago.  And, 
similarly,  for  the  fisherman,  the  temperature,  direction 
of  the  wind,  its  rising  or  falling,  etc.,  are  all  signs  from 
which  he  is  able  to  infer,  more  or  less  correctly,  the 
kind  of  weather  which  may  be  expected.  A  person 
who  had  no  systematic  knowledge  in  either  of  these 
fields,  would,  however,  see  nothing  in  the  scarred  rocks, 
or  in  the  sudden  change  of  the  wind ;  he  might  notice 
the  facts,  but  would  not  be  able  to  use  them  as  a  basis  of 
inference. 

It  is  important  to  notice  that  what  has  just  been  said  goes  to 
confirm  our  previous  statements  regarding  the  increasing  degree  of 
integration  which  knowledge  shows  in  the  course  of  its  development. 
The  knowledge  of  the  scientist  differs  from  that  of  the  ordinary  man, 
not  only  in  the  greater  number  of  facts  which  the  former  contains,  but 
also,  as  we  have  seen,  in  the  degree  of  integration  or  coherence 
which  these  facts  possess.  Inference,  then,  is  simply  a  deep  insight, 
based  on  definite  knowledge,  into  the  necessary  connection  of  things. 
It  is  an  act  of  thought  which  discovers  the  essential  relations  be- 
tween things  which  at  first  sight  appear  to  have  no  connection  with 
each  other.  As  has  already  been  said,  it  is  a  reasoned  judgment ; 
i.e.,  a  judgment  which  has  become  conscious  of  the  reasons  for  the 
connections  which  it  affirms. 

§  88.  Induction  and  Deduction.  —  It  has  been  already 
pointed  out  that  there  are  two  directions  in  which  infer- 
ence or  reasoning  may  proceed.  We  may  begin  with 
certain  facts  or  principles  which  are  already  known, 


330  THE  NATURE  OF  INFERENCE 

or  are  assumed  to  be  true,  and  proceed  to  show  that 
some  result  necessarily  follows  from  them.  Thus  we 
might  infer  that  if  the  draughts  of  a  stove  are  closed  so 
that  the  supply  of  oxygen  is  lessened,  the  fire  will  burn 
slowly ;  or  from  the  relative  positions  and  revolutions  of 
the  planets,  that  an  eclipse  of  the  sun  will  take  place  on 
a  specified  day  and  hour.  This  method  of  reasoning  is 
known  as  Deduction.  It  proceeds,  as  we  have  seen, 
from  premises  to  conclusion.  In  the  first  part  of  this 
book,  this  form  of  reasoning  has  been  treated  at  some 
length  and  its  rules  of  procedure  stated.  At  present, 
we  need  only  notice  that  in  deductive  reasoning  the  par- 
ticular case  is  always  brought  under  some  general  law 
or  principle,  which  is  already  known  or  assumed  as  true. 
Socrates  is  known  to  be  mortal,  because  as  a  man  he 
falls  under  the  general  law  that  all  men  are  mortal ;  the 
closing  of  the  draughts  is  a  case  of  lessened  supply  of 
oxygen,  and,  therefore,  in  accordance  with  the  general 
law,  a  case  of  slow  burning.  A  deductive  inference 
shows  what  are  the  results  of  the  application  of  a  gen- 
eral law  to  particular  facts  or  instances.  It  proceeds 
downwards,  as  it  were,  from  the  general  law  to  its  con- 
sequences. 

In  Induction,  on  the  contrary,  the  procedure  is  just 
the  opposite  of  this.  We  begin  with  particular 
phenomena,  and  try  to  discover  from  them  the  law 
or  principle  which  unites  them.  Certain  facts  are 
observed  to  happen  together,  and  the  problem  is  to 
find  the  ground  or  explanation  of  this  connection. 
Inductive  inference  is  thus  a  process  of  reading  the 
general  law  out  of  the  particular  facts.  It  is  an  insight 


§88.    INDUCTION  AND  DEDUCTION  331 

into  the  nature  of  the  whole  or  system,  based  upon  a 
careful  examination  of  the  parts.  '  Yesterday  the  smoke 
tended  to  fall  to  the  ground,  and  it  rained  in  the  after- 
noon.' These  two  facts  may  simply  be  observed  a 
number  of  times  without  any  thought  of  their  con- 
nection. But  intelligence  asks :  Why  should  they 
happen  in  conjunction  ?  And  to  answer  this  question, 
we  must  begin  by  analyzing  the  facts  in  our  possession. 
When  the  smoke  falls  to  the  ground,  the  atmosphere 
must  be  lighter  than  usual;  this  is  the  case  when  it 
contains  a  great  deal  of  moisture ;  but  when  the 
atmosphere  is  in  this  condition,  it  usually  tends  to 
discharge  its  moisture  in  the  form  of  rain ;  therefore 
we  have  the  general  law  which  enables  us  to  show  that 
the  behaviour  of  the  smoke  and  the  rain  yesterday  were 
not  only  accidentally  conjoined,  but  essentially  connected. 
Deduction  and  Induction,  then,  are  both  forms  of 
inference,  but  the  starting-point  and  mode  of  procedure 
of  the  one  is  different  from  that  of  the  other.  Conse- 
quently, it  is  not  unusual  to  speak  of  them  as  two  kinds 
of  reasoning  which  are  quite  distinct  and  independent 
of  each  other.  It  is,  however,  important  to  avoid  this 
popular  error,  and  to  remember  that  the  real  process  of 
inference  is  in  each  case  the  same.  The  essence  of 
inference,  as  has  been  shown,  consists  in  the  fact  that 
it  exhibits  the  manner  in  which  particular  facts  are 
connected  together  into  a  system  or  whole.  And  this 
end  is  achieved  both  by  Deduction  and  Induction.  In 
the  former  case,  the  general  law  of  connection^- what 
we  may  call  the  nature  of  the  system  within  which  the 
particulars  fall  —  is  known,  and  we  argue  from  this  as 


332  THE  NATURE  OF  INFERENCE 

to  the  nature  and  relations  of  the  various  parts  which 
fall  within  it.  We  have  the  common  thread  which 
unites  the  various  facts  in  our  hand,  and  following  it  out 
are  able  to  show  its  application  in  determining  the 
nature  of  events  which  have  not  yet  come  within  the 
range  of  our  experience.  Knowing  the  law  of  gravity, 
for  example,  one  could  infer  deductively  what  momentum 
a  ball  weighing  one  pound  must  necessarily  have  after 
falling  one  hundred  feet.  It  would  not  be  necessary 
actually  to  measure  the  momentum  of  the  falling  body 
in  this  particular  case,  but  it  could  be  shown  to  be  the 
necessary  result  of  the  general  law.  What  the  deductive 
inference  shows  to  us,  is  the  way  in  which  a  general 
principle  or  law  of  connection  runs  through  a  group  of 
facts,  and  constitutes  them  a  real  or  organic  whole. 
The  same  insight  is  reached  by  inductive  inference, 
although  the  starting-point  is  entirely  different.  As 
we  have  already  seen,  induction  begins  by  observing 
that  certain  phenomena  are  frequently  conjoined,  and 
attempts  to  discover  some  law  or  principle  which  will 
make  the  fact  of  their  connection  intelligible. 

It  is  usual  to  say  that  in  induction  we  go  from  the 
particular  facts  to  the  general  law.  The  following,  how- 
ever, would  be  a  more  correct  form  of  statement : 
Before  the  inference,  we  observe  that  a  number  of  phe- 
nomena occur  together,  but  do  not  know  whether  this 
conjunction  is  necessary  or  not ;  or,  if  we  assume  that 
it  is  necessary,  we  do  not  understand  why  it  should  be 
so.  As  a  result  of  the  inductive  inference,  we  gain  an 
insight  into  the  necessary  connection  of  the  observed 
phenomena,  and  also  understand  the  principle  according 


§  88.     INDUCTION  AND   DEDUCTION  333 

to  which  the  latter  are  united.  What  we  really  obtain 
through  an  inductive  inference  is  not  only  a  general  law, 
but  also  a  perception  of  its  concrete  application  to 
particular  phenomena.  This  being  so,  it  is  clear  that 
Induction  and  Deduction  are  not  two  different  kinds  of 
inference.  Inference  always  implies  an  effort  on  the 
part  of  the  mind  to  see  how  phenomena  are  neces- 
sarily connected  according  to  some  general  principle. 
And,  in  carrying  out  this  purpose,  the  mind  must  begin 
with  the  knowledge  which  it  already  possesses.  When 
the  general  law  of  connection  is  known,  and  the  object 
is  to  discover  the  nature  of  some  particular  fact,  the 
method  of  procedure  is  deductive.  But,  when  the 
problem  by  which  we  are  confronted  is  to  read  out  of 
the  facts  of  sense-perception  the  general  law  of  their 
connection,  the  method  of  inference  which  must  be 
employed  is  that  of  induction.  But  from  whatever 
point  we  set  out,  and  whatever  may  be  the  immediate 
object  of  the  inference,  the  result  is  always  the  same  — 
an  insight  into  the  necessary  connection  of  facts  accord- 
ing to  some  general  principle. 

It  is  not  unusual  to  hear  the  remark  made  that 
modern  science  has  been  built  up  by  the  employment 
of  the  inductive  method.  This  must  not,  however,  be 
interpreted  to  mean  that  deductive  inferences  are  not 
also  used  in  the  discovery  of  scientific  truth.  Science 
(which  is  simply  another  name  for  systematic  know- 
ledge) is  the  product  of  thinking,  and  thought,  as  we 
have  seen,  is  not  limited  to  any  one  mode  of  procedure. 
Thought  aims  at  extending  knowledge,  and  so  long  as 
it  can  find  any  link  of  connection,  or  guiding  thread,  it 


334  THE  NATURE  OF  INFERENCE 

is  hot  limited  to  any  one  direction,  or  to  any  fixed  mode 
of  working.  It  is,  of  course,  to  be  admitted  —  and 
this  is  what  is  true  in  the  statement  which  we  have 
quoted  —  that  general  laws  cannot  be  discovered  with- 
out an  examination  of  particular  facts,  and  that  their 
validity  must  always  be  tested  by  comparison  with  the 
facts.  But  as  soon  as  a  general  law  is  discovered  in 
any  field,  it  is  always  used  as  a  principle  from  which  to 
deduce  new  results.  When  it  is  possible  to  employ 
mathematics  in  the  calculation  of  these  results,  it  is 
usually  possible  to  extend  our  knowledge  of  the  subject 
much  more  rapidly  than  before.  Thus  physics  and 
astronomy  owe  their  rapid  development  to  the  applica- 
tion of  mathematics.  It  must  be  remembered,  however, 
that  this  presupposes  a  certain  stage  of  advancement  — 
a  certain  inductive  stage,  as  it  were  —  on  the  part  of 
the  science..  But  even  in  this  earlier  stage,  we  are 
constantly  employing  deduction, — reasoning  out  the 
results  of  certain  guesses  or  suggestions  to  see  if  they 
hold  true  (cf.  §  47).  Both  in  ordinary  life,  and  in 
scientific  procedure,  we  may  see,  Induction  and  Deduc- 
tion are  constantly  employed  together. 

References 

i 

B.  Bosanquet,  Logic,  Vol.  II.  Ch.  I. 

F.  H.  Bradley,  The  Principles  of  Logic,  pp.  430-468. 

W.  James,  The  Principles  of  Psychology,  Vol.  II.  Ch.  XXII. 

J.  G.  Hibben,  Inductive  Logic,  Chs.  I.  and  II. 


CHAPTER   XXV 

RATIONAL    AND    EMPIRICAL    THEORIES 

§  89.  The  Point  of  View  of  Rationalism.  —  In  the  his- 
torical sketch  of  logic  given  in  Chapter  II.,  it  was  stated 
that  there  are  two  rival  accounts  of  the  nature  of  know- 
ledge, and  the  methods  by  which  it  is  attained  (cf.  §  8). 
The  first  of  these  theories  is  known  as  Rationalism,  and 
has  its  best  known  historical  representative  in  Descartes; 
while  Empiricism,  the  opposing  theory,  is  associated  with 
the  names  of  the  great  thinkers,  Bacon  and  Locke. 
The  doctrines  of  both  these  schools  have  been  fre- 
quently modified,  and  the  contrast  between  them  is 
now  no  longer  so  pronounced  as  it  was  formerly.  In 
spite  of  this  fact,  however,  the  division  has  always 
represented  two  schools  of  thought  whose  general  re- 
lations to  each  other  have  remained  comparatively  con- 
stant. In  general,  too,  it  has  been  true  that  English 
thinkers  have  upheld  Empiricism,  while  Rationalism 
has  had  its  home  on  the  Continent  —  at  first  in  France, 
and  later  in  Holland  and  Germany. 

Rationalism  regards  mathematics  as  the  type  of  all 
knowledge.  Its  essential  characteristic  consists  in  the 
fact  that  it  undertakes  to  derive  all  knowledge  from 
general  principles.  These  principles  have  sometimes 
been  regarded  as  innate  (truths  which  are  stamped 
upon  the  mind  at  birth),  or  it  has  been  supposed  that 

335 


336  RATIONAL  AND    EMPIRICAL  THEORIES 

they  are  in  some  way  known  before  experience,  and 
have  a  right  to  the  title  of  a  priori  propositions  (§  76). 
Notwithstanding  the  various  forms  in  which  their  theo- 
ries have  been  expressed,  all  rationalistic  thinkers  agree 
in  regarding  the  first  principles  upon  which  our  know- 
ledge is  based,  as  upon  a  different  plane  from  the  facts 
of  ordinary  life.  While  the  latter  are  known  only  by 
experience,  and  may  be  wholly  or  partially  false,  the 
former  are  described  as  principles  which  are  in  them- 
selves necessary,  truths  the  opposite  of  which  is  incon- 
ceivable, or  sometimes  as  the  axioms  presupposed  in  all 
experience.  These  principles  being  accepted,  the  prob- 
lem which  lay  before  Rationalism  was  to  show  how  all 
the  facts  of  our  experience  necessarily  follow  from 
them,  just  as  the  various  propositions  of  geometry 
follow  from  the  definitions  and  axioms  which  are  as- 
sumed as  the  starting-point.  As  a  matter  of  fact,  how- 
ever, the  famous  Jewish  thinker,  Spinoza  (1632-1677), 
was  the  only  man  who  ever  attempted  to  carry  out 
Rationalism  in  this  systematic  form.  In  general,  one 
may  say  that  rationalistic  thinkers  have  been  mainly 
interested  to  show  that  the  facts  of  the  moral  and  reli- 
gious experience  are  logically  derivable  from  certain 
necessary  first  principles.  It  was  questions  like  those 
regarding  the  existence  of  God,  the  immortality  of  the 
soul,  and  the  freedom  of  the  will,  which  the  rationalists 
were  anxious  to  put  beyond  dispute.  And,  as  a  con- 
sequence, not  nearly  the  same  amount  of  effort  was 
devoted  to  showing  how  the  other  facts  of  experience 
could  be  similarly  derived  from  general  principles. 
It  will  be  at  once  clear,  from  what  has  been  already 


§  90.     THE   DOCTRINE  OF   EMPIRICISM  337 

said,  that  the  great  instrument  of  knowledge  from  this 
standpoint  must  be  reason.  Very  little  attention  is  paid 
to  perception,  and  the  experience  which  it  furnishes  is 
not  regarded  as  entitled  to  the  name  of  knowledge. 
In  order  to  know,  in  the  true  sense  of  the  word,  it  is 
necessary  to  show  the  systematic  connection  of  every 
fact  with  some  fundamental  first  principle ;  and  this, 
of  course,  can  be  done  only  by  the  employment  of 
reasoning.  Perception  gives  us  only  the  bare  facts  ;  it 
is  reason  which  enables  us  to  trace  the  mutual  connec- 
tions, and  derivation  of  these  facts  from  some  general 
law.  The  weakness  of  the  rationalistic  position  does  not 
consist  in  its  insistence  on  the  necessity  of  connecting 
the  particular  facts  of  experience  with  general  laws  or 
principles,  but  in  the  assumption  upon  which  it  pro- 
ceeded that  these  principles  could  themselves  be  derived 
from  some  other  source  than  experience.  The  result 
was  that  the  rationalists  employed  themselves  too  ex- 
clusively in  deducing  facts  from  general  propositions 
which  were  assumed  to  be  true  without  sufficient  criti- 
cism and  examination.  They  saw  clearly  enough  that 
mere  perception  without  general  principles  can  never 
give  us  knowledge,  but  they  did  not  understand  that  it 
is  impossible  to  separate  the  latter  from  the  former, 
and  to  regard  principles  as  existing  in  the  mind  prior 
to  experience. 

§  90.  The  Doctrine  of  Empiricism.  —  Empiricism  main- 
tains that  all  knowledge  is  derived  from  experience  ;  and 
by  experience  is  understood  the  separate  unconnected 
facts  with  which  the  mind  is  furnished  in  perception. 


338  RATIONAL  AND   EMPIRICAL  THEORIES 

Empiricism  refuses  to  admit  that  we  possess  any 
store  of  first  principles  or  general  truths  which  are 
native  to  the  mind,  or  are  obtained  from  any  other 
source  than  experience.  It  is  impossible  for  the  mind 
to  know  anything  of  which  it  has  had  no  perception. 
Moreover,  the  very  fact  that  perception  is  made  the 
standard  of  knowledge,  led  to  the  belief  that  the  mind 
is  something  essentially  passive,  upon  which  ideas  are 
impressed  by  external  forces.  Empiricism  regards 
knowledge  as  the  sum  of  the  particular  facts  furnished 
to  the  mind  through  sense,  not  as  a  system  which  is 
the  product  of  the  mind's  own  activity.  As  a  conse- 
quence, there  results  an  entirely  different  theory  of 
knowledge  from  that  which  we  have  given  in  this  book. 
Ideas  are  supposed  to  be  furnished  to  the  mind  by 
the  channel  of  the  senses,  or  are  compounded  from 
simpler  elements  which  are  supplied  in  this  way.  And 
when  ideas  become  united  by  standing  in  juxtaposition, 
or  being  associated  in  some  other  way,  the  result  is  a 
judgment.  In  this  account,  the  judging,  or  interpreting 
activity  of  the  mind,  which  we  have  made  the  source 
of  all  knowledge,  is  wholly  omitted.  Indeed,  one  may 
say  that  empirical  theories  undertake  to  explain  know- 
ledge without  reference  to  the  mind  and  its  mode  of 
activity.  Although  all  empirical  thinkers  do  not  deny 
the  existence  of  the  mind,  yet  none  of  them  wish  to  go 
beyond  the  particular  facts,  and  to  call  in  its  aid  as  a 
principle  of  explanation. 

The  same  insistence  upon  particular  facts,  and 
avoidance  of  general  principles,  is  characteristic  of 
empirical  theories  of  reasoning.  All  inference,  it  is 


§  90.    THE   DOCTRINE   OF   EMPIRICISM  339 

maintained,  is  based  upon  a  perception  of  resem- 
blance between  individual  cases.  The  general  law, 
or  principle,  is  nothing  in  itself  but  an  abbreviated 
statement  of  the  manner  in  which  all  the  instances 
act  which  we  have  hitherto  observed.  The  clearest 
statement  of  this  theory  is  given  by  John  Stuart 
Mill,  from  whose  work  on  Logic  the  following  pas- 
sages are  taken :  "  Now,  all  which  man  can  observe 
are  individual  cases.  From  these  all  general  truths 
must  be  drawn,  and  into  these  they  may  again  be 
resolved;  for  a  general  truth  is  but  an  aggregate  of 
particular  truths,  a  comprehensive  expression  by  means 
of  which  an  indefinite  number  of  individual  facts  are 
affirmed  or  denied  at  once.  .  .  .  From  instances  which 
we  have  observed,  we  feel  warranted  in  concluding  that 
what  we  found  true  in  those  instances  holds  in  all  simi- 
lar ones,  past,  present,  and  future,  however  numerous 
they  may  be.  ...  When,  therefore,  we  conclude  from 
the  death  of  John  and  Thomas,  and  every  other  person 
we  ever  heard  of  in  whose  case  the  experiment  had 
been  fairly  tried,  that  the  Duke  of  Wellington  is  mortal 
like  the  rest,  we  may  indeed  pass  through  the  generali- 
zation, All  men  are  mortal,  as  an  intermediate  stage  ; 
but  it  is  not  in  the  latter  half  of  the  process,  the  descent 
from  all  men  to  the  Duke  of  Wellington,  that  the  infer- 
ence resides.  The  inference  is  finished  when  we  have 
asserted  that  all  men  are  mortal.  What  remains  to  be 
performed  afterwards  is  merely  deciphering  our  own 
notes." *  In  other  words,  Mill  maintains  that  all  in- 
ference is  based  upon  the  perception  of  particular 

1  Mill,  Logic,  Bk.  II.  Ch.  III.  §  3. 


340  RATIONAL  AND   EMPIRICAL  THEORIES 

cases.  There  is  no  such  a  thing  as  reasoning  from 
general  truths  or  principles.  We  may,  indeed,  arrive 
at  such  general  truths  by  repeated  experiences,  and 
store  them  up  as  maxims  in  our  memory  ;  but  they  are 
not  at  all  necessary  for  the  process  of  inference,  which 
may  be  said  to  be  always  inductive  in  character,  since 
it  sets  out  from  a  perception  of  individual  cases.  "  In- 
duction, properly  so  called,  .  .  .  may  be  defined  as  a 
generalization  from  experience.  It  consists  in  inferring 
from  some  individual  instances  in  which  a  phenome- 
non is  observed  to  occur,  that  it  occurs  in  all  instances 
of  a  certain  class ;  namely,  in  all  which  resemble  the 
former  in  what  are  regarded  as  the  material  circum- 
stances." x 

This  account  of  the  way  in  which  inference  proceeds 
undoubtedly  contains  much  that  is  true.  Nevertheless, 
it  is  not,  I  think,  an  adequate  statement  of  the  nattire  of 
inference.  What  one  misses  chiefly  is  some  insistence 
upon  the  fact  that  it  is  only  in  virtue  of  some  identical 
link,  or  common  element,  which  is  present  in  all  the 
individual  cases,  that  one  is  able  to  pass  from  one  to 
another.  On  this  point  we  must  refer  to  what  was  said 
in  the  last  chapter  (§  87).  It  will  perhaps  be  possible 
to  gain  a  clearer  idea  of  what  is  true  and  what  is  false 
in  this  theory,  by  considering  further  Mill's  doctrine, 
that  it  is  possible  to  reason  from  one  particular  fact  to 
another,  without  any  reference  to  general  truths. 

§  91.  Reasoning  from  Particulars  to  Particulars.  —  "  Not 
only  may  we  reason  from  particulars  to  particulars,  with- 

1  Mill,  Logic,  Bk.  III.  Ch.  III.  §  I. 


§91.     FROM   PARTICULARS  TO   PARTICULARS        341 

out  passing  through  generals,  but  we  perpetually  do  so 
reason.  All  our  earliest  inferences  are  of  this  nature.' 
From  the  first  dawn  of  intelligence  we  draw  inferences, 
but  years  elapse  before  we  learn  the  use  of  general 
language.  The  child,  who,  having  burned  his  fingers, 
avoids  to  thrust  them  again  into  the  fire,  has  reasoned 
or  inferred,  though  he  never  thought  of  the  general 
maxim,  Fire  burns.  He  knows  from  memory  that  he 
has  been  burned,  and  on  this  evidence  believes,  when 
he  sees  a  candle,  that  if  he  puts  his  finger  into  the  flame 
of  it,  he  will  be  burned  again.  He  believes  this  in  any 
case  which  happens  to  arise,  but  without  looking  in 
each  instance  beyond  the  present  case.  He  is  not  gen- 
eralizing ;  he  is  inferring  a  particular  from  particulars. 
...  It  is  not  only  the  village  matron,  who,  when  called 
to  a  consultation  on  the  case  of  a  neighbour's  child,  pro- 
nounces on  the  evil  and  its  remedy  on  the  recollection 
and  authority  of  what  she  accounts  the  similar  case  of 
her  Lucy.  We  all,  when  we  have  no  definite  maxims 
to  steer  by,  guide  ourselves  in  the  same  way."  1 

The  doctrine  as  thus  stated  by  Mill  is  the  extreme 
opposite  of  Rationalism.  Not  only  are  all  general 
propositions  derived  from  observation  of  particular  in- 
stances, but  they  play  no  part  in  the  process  of  infer- 
ence proper.  All  reasoning,  according  to  this  account, 
is  based  on  the  perception  of  resemblance  between 
individual  cases.  No  common  nature  or  general  prin- 
ciple seems  necessary  to  unite  the  latter  into  a  system. 

Nevertheless,  it  must  be  confessed  that  Mill's  state- 

1  Mill,  Logic,  Bk.  II.  Ch.  III.  §  3. 


342  RATIONAL  AND   EMPIRICAL  THEORIES 

ment  affords  an  excellent  account  of  many  of  our 
ordinary  inferences.  We  may  accept  it,  however,  as  a 
description  of  fact  without  committing  ourselves  to  the 
theory  which  it  contains.  That  is,  it  will  still  be  neces- 
sary to  ask  if  inference  is  not,  after  all,  based  on  the 
perception  of  some  general  law  or  principle,  although 
it  is  not  always  possible  to  formulate  the  nature  of 
the  latter.  It  does  not  seem  to  me  that  the  nature  of 
the  inference  in  the  cases  cited  is  completely  described 
when  it  is  said  to  be  a  passage  from  one  particular 
case  to  another  which  resembles  it.  For  it  is  necessary 
to  look  further,  and  to  see  what  is  implied  in  the  fact 
that  one  case  is  perceived  to  resemble  another.  When 
the  child  perceives  that  the  bright  object  before  him 
resembles  something  which  previously  gave  him  pain, 
he  has  got  beyond  the  merely  individual  aspect  of 
things,  and  is  beginning  to  regard  them  as  types  or 
instances  of  a  general  law.  Of  course,  the  child  is 
not  fully  conscious  of  any  general  principle.  He  does 
not  separate  the  latter  from  its  embodiment  in  the  par- 
ticular case,,  or  put  it  into  language  even  to  himself. 
But,  in  order  to  infer,  one  must  take  the  individual 
case  as  something  more  than  a  mere  particular,  as  this 
which  is  only  here  and  now.  In  the  child's  perception 
of  resemblance  between  the  present  object  and  the  one 
previously  experienced,  there  is  an  implicit  reference  to 
a  permanent  type,  or  identity  which  persists  through 
the  two  cases.  In  other  words,  when  one  asks  what  a 
perception  of  resemblance  means,  one  sees  that  it  im- 
plies an  apprehension  on  the  part  of  intelligence  of 
something  which  is  more  than  merely  momentary. 


§91.    FROM   PARTICULARS  TO  PARTICULARS        343 

The  same  quality  or  other  element  which  is  found  in 
that  object  is  also  found  in  this.  And  the  inference 
proceeds,  that  object  was  hot,  therefore  this  object 
(having  the  same  general  nature,  or  being  of  the  same 
type)  is  also  hot.  It  is,  of  course,  frequently  impossible 
to  formulate  clearly  the  nature  of  the  principle  upon 
which  we  proceed,  and,  in  cases  like  those  cited,  one  may 
not  be  aware  that  it  is  present.  But,  I  hope,  it  will  now 
be  clear  that  even  in  such  instances  the  inference  is 
based  upon  a  permanent  nature  present  in  the  two  cases. 
We  have  already  seen  that  where  such  an  identical  link 
is  not  present,  it  is  impossible  to  pass,  by  means  of  in- 
ference, from  a  knowledge  of  one  thing  to  another.  As 
mere  particulars,  two  phenomena  occurring  at  different 
times  are  entirely  isolated,  and  have  nothing  to  do 
with  each  other.  But  as  pieces  of  knowledge,  facts 
which  have  been  constituted  by  the  interpreting  func- 
tion of  Judgment,  they  are  bound  together  by  a  com- 
mon principle,  the  nature  of  a  whole  or  system.  This 
principle  is,  indeed,  not  anything  apart  from  the  facts 
connected,  or  in  any  way  prior  to  them  ;  but  neverthe- 
less something  without  which  it  would  be  impossible  to 
understand  their  connection. 

The  conclusion  of  the  matter,  then,  is  that  we  never 
reason  from  one  bare  particular  to  another  particular. 
More  than  that,  we  may  say  a  fact  which  is  merely 
particular  —  something  which  is  only  here  and  now  — 
has  no  existence  in  knowledge.  For  knowledge  lays 
hold  of  the  universal  aspect  of  things,  their  permanent 
significance.  Intelligence  sees  the  universal  or  typical 
nature  in  what  is  for  sense  a  fleeting  phenomenon.  It 


344  RATIONAL  AND   EMPIRICAL  THEORIES 

is  only  when  the  facts  of  sense  are  interpreted  in  this 
way,  when  their  real  nature  is  apprehended  by  thought, 
that  they  can  be  said  to  be  known  at  all.  Knowledge 
sees  the  universal  in  the  particular,  or  reads  the  partic- 
ular as  a  case  of  the  universal.  And  when  thus  inter- 
preted, the  particular  ceases  to  be  a  bare  particular,  and 
becomes  an  individual  with  a  permanent  nature  of  its 
own.  When  one  reasons  from  an  individual  case,  then, 
it  is  the  universal  or  typical  nature,  not  the  particular 
or  momentary  existence,  upon  which  the  inference  pro- 
ceeds. If  there  were  any  merely  particular  facts  in 
knowledge,  we  could  never  reason  from  them.  But,  as 
has  been  shown,  the  so-called  particular  facts,  as  ele- 
ments of  knowledge,  possess  a  universal  or  typical  as- 
pect in  virtue  of  which  alone  inference  is  possible. 

§  92.   Reasoning  from  Individual  Cases  to  a  Universal. 

-There  remains  another  question  which  is  very  closely 
related  to  the  points  already  discussed  in  this  chapter. 
We  must  admit  that  in  inductive  inference  at  least  the 
starting-point  is  individual  instances,  though,  as  the  last 
section  showed,  the  latter,  as  used  in  reasoning,  are 
something  more  than  mere  particulars.  The  problem 
which  meets  us,  however,  is  this :  How  is  it  ever  pos- 
sible to  get  a  universal  conclusion  from  individual 
instances  ?  It,  of  course,  frequently  happens  that  we 
cannot  examine  all  the  cases.  What  right  then  have 
we  in  these  circumstances  to  state  our  conclusion 
generally  —  to  assert,  for  example,  that  'all  men  are 
mortal,'  or  '  all  mosses  cryptogams  '  ? 

It  is  often  said  that  in  such  cases  the  general  con- 


§  92.     FROM   PARTICULARS  TO  A  UNIVERSAL        345 

elusion  is  never  more  than  probable,  and  that  its  proba- 
bility increases  directly  in  proportion  to  the  number  of 
instances  examined.  Thus  if  A  and  B  are  conjoined  only 
once  in  my  experience,  it  is  very  improbable  that  the 
connection  is  a  universal  and  essential  one.  But  if  they 
are  found  together  ten  times,  the  proposition,  '  A  is  B  ' 
begins  to  have  probability,  which  is,  of  course,  greatly 
increased  (without  ever  becoming  more  than  probable 
however),  if  the  conjunction  is  observed  a  hundred,  or  a 
thousand  times.  Now,  there  can  be  no  doubt  that  the 
frequency  of  conjunction  is,  to  a  certain  extent,  a  prac- 
tical test  of  real  or  universal  connection.  Belief,  as  a 
psychological  fact,  is  engendered  by  frequency  of  repeti- 
tion. But  the  causes  of  our  belief  are  here,  as  in  many 
cases,  quite  different  from  the  real  or  logical  grounds. 
The  fact  that  two  phenomena  have  occurred  together  a 
hundred  times,  in  itself  affords  no  logical  ground  for 
afBrming  a  universal  connection  between  them,  or  that 
they  will  be  connected  the  hundred  and  first  time.  Of 
course,  as  we  have  said,  psycJiological  belief  or  expecta- 
tion would  be  engendered  by  the  frequent  conjunction  ; 
but  the  latter  would  supply  no  real  or  logical  grounds. 
Practically,  we  are  more  certain  to  be  right,  if  we  gen- 
eralize on  the  basis  of  a  large  number  of  observations, 
than  if  we  proceed  on  the  authority  of  a  smaller  num- 
ber. But,  as  affording  logical  justification  for  our  pro- 
cedure, a  hundred  instances  (if  they  are  merely  counted) 
are  no  better  than  one. 

The  truth  is  that  a  general  conclusion  does  not  de- 
pend for  its  logical  justification  upon  the  number  of 
instances  observed.  Inference  is  not  a  matter  of  count- 


346  RATIONAL  AND   EMPIRICAL  THEORIES 

ing  instances  at  all,  but  is  an  intellectual  insight  into 
the  nature  of  a  general  law  or  principle  of  connection. 
The  problem  of  inductive  inference  is  to  discover  this 
principle  in  the  individual  case,  to  penetrate  beneath 
the  surface,  and  read  out  o'f  the  individual  phenome- 
non its  real  meaning  or  significance.  To  accomplish 
this  usually  requires  an  examination  of  many  particu- 
lar cases.  We  have  more  chances  of  learning  the 
secret  fully  if  we  take  as  wide  a  survey  as  possible 
of  the  facts.  A  generalization  based  upon  a  small 
number  of  observations  is  pretty  sure  to  be  incorrect 
or  inaccurate.  But  though  of  such  great  practical  im- 
portance, the  number  of  instances  is  logically  indiffer- 
ent. The  essential  point  is  to  detect  the  general  law  or 
principle,  and  for  this  purpose  one  case  may  conceiva- 
bly be  as  good  as  a  hundred.  Inductive  inference, 
then,  is  not  a  process  of  passing  from  a  certain  number 
of  cases  to  a  general  conclusion  which  always  remains 
probable  because  it  has  no  proper  justification.  But  its 
real  nature  consists  in  the  discovery,  through  the  aid  of 
examples,  of  a  universal  law  of  connection.  We  have 
already  shown  the  part  which  the  constructive  imagina- 
tion, guided  by  Analogy,  plays  in  reaching  this  result 
(cf.  §§  60,63). 

It  must  be  admitted  that  there  are  many  cases  where  it  is  impossi- 
ble to  get  beyond  the  fact  that  two  phenomena  are  constantly  con- 
joined in  our  experience.  The  grounds  which  should  make  this  fact 
intelligible  lie  beyond  our  ken.  Under  circumstances  of  this  kind, 
we  are,  of  course,  compelled  to  act  on  the  presumption  that  the  same 
order  of  events  will  continue  to  obtain.  We  may  find  that  a  certain 
medicine  is  followed  by  certain  physiological  consequences,  without 


§92.     FROM   PARTICULARS  TO  A   UNIVERSAL        347 

being  able  to  discover  anything  regarding  the  way  in  which  the  lat- 
ter have  been  produced.  And  we  may  confidently  predict  that  the 
same  results  will  follow  in  a  new  case  where  the  same  medicine  has 
been  given.  But  it  must  be  noticed  that  this  is  not  the  ideal  of  rea- 
soning. Knowledge  of  the  kind  we  have  described  is  merely  em- 
pirical, follows  a  rule  of  thumb  without  being  able  to  give  any  account 
of  itself.  Moreover,  even  in  such  cases,  it  is  always  assumed  that 
there  is  some  general  principle  or  law  which  may  yet  be  discovered, 
and  which  is  capable  of  explaining  the  facts  known  empirically. 

References 

J.  S.  Mill,  Logic,  Bk.  II. 

H.  Spencer,  Principles  of  Psychology,  §  208. 

W.  James,  The  Principles  of  Psychology,  Vol.  II.  Ch.  XXVIII. 

B.  Bosanquet,  Logic,  Vol.  II.,  pp.  176-179. 


QUESTIONS   AND   EXERCISES 

INTRODUCTION 

CHAPTER  I.  —  The  Standpoint  and  Problem  of  Logic 

1.  What  are  some  of  the  main  characteristics  of  thought  or 
thinking  ? 

2.  Explain  the  use  of  the  verb  to  think  in  each  of  the  fol- 
lowing sentences  :  '  I  do  not  know,  but  I  think  so ; '  *  If  you 
think  the  matter  over,  you  will  come  to  the  same  conclusion.' 

3.  '  Words  and  phrases  are  often  repeated  without  reflection, 
and  their  very  familiarity  is  likely  to  prevent  us  from  attempting 
to  understand  exactly  what  ideas  they  represent.'     Give  illus- 
trations of  this  fact. 

4.  What  do  you  mean  by  a  science  ?     How  does  '  scientific  ' 
knowledge  differ  from  the  knowledge  of  ordinary  life? 

5.  What  is  the  meaning  of  the  word  Maw'  in  the  phrase 
1  a  law  of  thought '  ?     Compare  the  use  of  the  word  in  such  ex- 
pressions as  '  laws  of  nature,'  '  the  laws  of  the  land.' 

6.  Is  it  true  that  Logic  and   Psychology  have   the   same 
subject-matter? 

7.  Explain  carefully  how  the  problem  of  Logic  differs  from 
that  of  Psychology. 

8.  If  we  parallel  Psychology  with  Morphology,  and  Logic 
with    Physiology,    what    mental   science    will    correspond    to 
Embryology  ? 

9.  Illustrate  by  means  of  examples  not  used  in  the  text  the 
relation  in  which  science  and  art,  or  theory  and  practice,  stand 
to  each  other. 

348 


QUESTIONS   AND    EXERCISES  349 

10.  Criticise  the  following  statement :  '  Logic  is  not  only  a 
science ;  it  is  also  an  art,  for  it  teaches  us  to  reason  correctly.' 

1 1 .  What  part  does  Introspection  play  in  investigating  logi- 
cal questions? 

12.  In  what  sense  may  we  say  that  the  records  of  everything 
which  the  human  race  has  accomplished  form  the  material  of 
Logic  ? 

CHAPTER  II.  —  Historical  Sketch 

1.  'The  sciences  have  arisen  in  response  to  the  practical 
needs  of  mankind.'     Is  this  statement  confirmed  by  the  history 
of  the  origin  and  development  of  Logic  ? 

2.  '  Since  each  individual  sees  things  from  his  own  point  of 
view,  there  is  therefore  nothing  really  true  in  itself,  or  good  in 
itself.'     Give  some  illustrations  of  the  former  part  of  this  state- 
ment.    What  term  would  you  use  to  describe  the  theory  which 
the  sentence  expresses  ? 

3.  Explain  what  is  meant  by  the  statement  that  Socrates 
and  Plato  found  a  standard  of  truth  and  of  conduct  in  the 
Concept. 

4.  Why  was  it  not  possible  for  Aristotle  to  lay  down  a  com- 
plete theory  of  Inductive  Reasoning? 

5.  What  is  Mill's  theory  regarding  the  relation  of  Induction 
and  Deduction? 

6.  Describe  the  standpoint  of  Modern  Logic. 

PART  I.  — THE  SYLLOGISMS 
CHAPTER  III.  —  The  Syllogism  and  its  Parts 

1.  Describe  the  general  purpose  and  nature  of  the  syllogism. 

2.  What  is  the  principle  upon  which  syllogistic  reasoning 
depends?     Why  is  it  impossible  to  reason  if  this  principle  is 
violated? 


350  QUESTIONS  AND   EXERCISES 

3.  Explain  the  distinction  between  the  formal  and  real  truth 
of  an  argument. 

4.  Arrange  the  following  sentences  as  logical  propositions, 
pointing  out  the  logical  Subject  and  the  Predicate  in  each 
case :  — 

(a)  Learning  taketh  away  the  wildness  of  men's  minds. 
(b  )   Dissipation  wastes  health. 

(c  )  The  exposition  of  a  principle  indirectly  contributes  to 
its  proof. 

(d)  To  me  the  meanest  flower  that  lives  can  give  thoughts 

that  do  often  lie  too  deep  for  tears. 

(e)  The  Alps  consist  of  several  parallel  ranges. 
(/)  The  travellers  had  found  the  city  in  ruins. 

5.  Point  out  the  Premises  and  Conclusion  in  the  following 
arguments,  and  supply  any  premise  which  may  be  wanting  :  — 

(a)  He  is  not  indifferent  to  money ;  for  he  is  a  sensible 
man,  and  no  sensible  man  despises  money. 

(b  )  All  human  productions  are  liable  to  error,  and  there- 
fore all  books,  being  human  productions,  are  liable 
to  error. 

(<:)  All  that  glitters  is  not  gold;  for  brass  glitters. 

(d)  All  bodies  which  move  round  the  sun  are  planets; 

therefore  the  earth  is  a  planet. 

(e)  Platinum   is  a  metal,  and  therefore  combines  with 

oxygen. 

6.  How  does  Jevons  describe  Simple  Apprehension?    Is  it 
possible  to  maintain  that  Apprehension,  Judgment,  and  Rea- 
soning are  three  distinct  operations  of  mind? 

CHAPTER  IV.  —  Terms 

i.   Distinguish  in  the   following  list  the  terms  which   are 
usually  (i)  Singular,  (2)  General,  and  (3)  Collective.     If  any 


QUESTIONS   AND   EXERCISES  351 

term  may  belong  to  more  than  one  class,  explain  and  illustrate 
its  various  uses  :  — 

Niagara  Falls,  an  oak  tree,  the  United  States  Navy, 

gold,  a  dancing  party,  Brooklyn  Bridge, 

chair,  the  United  States,  humanity, 

a  pack  of  cards,  city,  the  centre  of  the  earth. 

2.  Explain  and  illustrate  the  ambiguity  in  the  use  of  the 
word  '  all.' 

3.  In  what  two  ways  are  the  words  Abstract  and  Concrete 
used  ?     In  what  sense,  if  at  all,  can  we  say  that  Psychology  and 
Logic  are  i  abstract '  sciences  ? 

4.  Distinguish  carefully  between  Contradictory  and  Oppo- 
site terms. 

5.  What  are  Correlative  terms?     Give  at  least  three  ex- 
amples. 

6.  Mention  the  synonyms  for  Intension  and  Extension. 

7.  Explain  the  Extensional  and  Intensional  use  of  the  fol- 
lowing terms  :  — 

metal,  chair,  man,  Caesar,  superstition, 

justice,  student,  John  Jones,  island,  emperor. 

8.  Criticise   the  statement  that  '  Extension  and  Intension 
stand  in  inverse  ratio  to  each  other.'     What  truth  does  it  con- 
tain? 

9.  Invent  a  series  of  at  least  six  terms  which  may  be  ar- 
ranged so  as  gradually  to  increase  in  Extension. 

10.  What  may  be  said  in  reply  to  Mill's  contention  that 
proper  names  are  non-connotative? 

CHAPTER  V.  —  Definition  and  Division 

1.  Why  is  Definition  necessary? 

2.  What  is  the  distinction  between  extensive  and  intensive 
definition?     What  is  a  verbal  definition? 


352  QUESTIONS  AND   EXERCISES 

3.  In   what  two   ways   may  we   conceive  the   problem   of 
Definition? 

4.  What  do  you  understand  by  the  Socratic  Dialectic  ?    Ex- 
plain its  purpose  and  mode  of  procedure. 

5 .  Explain  the  terms  :  — 

genus,  differentia,  infima  species, 

species,  summum  genus,  sui  generis. 

6.  Criticise  the  following  definitions,  pointing  out  what  rules, 
if  any,  are  violated  by  them  :  — 

1 i )  Logic  is  the  science  of  thought. 

( 2 )  A  power  is  a  force  which  tends  to  produce  motion. 

(3)  Tin  is  a  metal  lighter  than  gold. 

(4)  A  gentleman  is  a  man  who  has  no  definite  means  of 

support. 

(5)  The  body  is  the  emblem  or  visible  garment  of  the 

soul. 

(6)  Man  is  a  vertebrate  animal. 

(7)  Thunder-bolts  are    the  winged  messengers   of  the 

gods. 

(8)  A  moral  man  is  one  who  does  not  lie  or  steal  or  live 

intemperately. 

(9)  Cheese  is  a  caseous  preparation  of  milk. 

(10)  Evolution  is  to  be  defined  as  a  continuous  change 

from  indefinite  incoherent  homogeneity  to  definite 
coherent  heterogeneity  of  structure  and  function, 
through  successive  differentiations  and  integra- 
tions (Spencer). 

( 1 1 )  Oats  is  a  grain  which  in  England  is  generally  given 

to  horses,  but  in  Scotland  supports  the  people. 

7.  Give  examples  of  terms  which  are  indefinable,  and  ex- 
plain why  this  is  the  case.     What  is  the  distinction  between 
Description  and  logical  Definition? 


QUESTIONS   AND   EXERCISES  353 

8.  Define  the  following  terms  by  giving  the  genus  and  dif- 
ferentia :  — 

science,  republic,  psychology,  island, 

triangle,  monarchy,  gold  standard,  import  duty. 

9.  Examine  the  following  Divisions  and  point  out  which  are 
logical  and  which  are  not :  — 

(1)  Living  beings  into  moral  and  immoral. 

(2)  Men  into  saints  and  sinners. 

(3)  Religions  into  true  and  false. 

(4)  Man  into  civilized  and  black. 

(5)  Geometrical  figures  into  rectilinear  and  non-recti- 

linear. 

(6)  Substances  into  material  and  spiritual. 

(7)  Metals  into  white,  heavy,  and  precious. 

(8)  Elementary   mental  processes   into  sensations  and 

affections. 

(9)  Students  into   those  who  are  idle,  those  who   are 

athletic,  and  those  who  are  diligent. 
(10)  Books  into  scientific  and  non-scientific. 

CHAPTER  VI.  —  Propositions 

1.  What  is  a  proposition?     In  what  sense  may  a  proposition 
be  said  to  have  parts? 

2.  Distinguish  between  Categorical  and  Conditional  propo- 
sitions. 

3.  What  is  meant  by  (a)  the  Quality,  and  (b)  the  Quantity, 
of  propositions? 

4.  Arrange  the  following  sentences  in  the  form  of  logical 
propositions,  and  indicate  the  Quality  and  Quantity  of  each 
categorical   proposition   by   the   use   of  the   letters   A,  E,  I, 
and   O:  — 


354  QUESTIONS  AND   EXERCISES 

(1)  Brevity   has   to  be  sought  without  sacrificing  per- 

spicuity. 

(2)  He  that  doeth  these  things  is  like  to  a  man  that 

buildeth  his  house  upon  a  rock. 

(3)  Socrates  declared  knowledge  to  be  virtue. 

(4)  Phosphorus  does  not  dissolve  in  water. 

(5)  Nearly  all  the  troops  have  left  the  town. 

(6)  Only  ignorant  persons  hold  such  opinions. 

(7)  Few  persons  are  proof  against  temptation. 

(8)  Over  the  mountains  poured  the  barbarian  horde. 

(9)  Except  ye  repent,  ye  shall  all  likewise  perish. 

(10)   Neither  gold  nor  silver  is  the  proper  standard  of 
value. 

5.  How  does  formal  logic  interpret  the  relation  between  the 
subject  and  predicate  of  a  categorical  proposition?     Does  this 
view  do  full  justice  to  the  signification  of  propositions? 

6.  How  would  you  represent  by  means  of  circles  the  propo- 
sition, '  gold  is  the  most  precious  metal '  ? 

7.  What  do  you  mean  by  the  distribution  of  terms  ?     Explain 
why  negative  propositions  distribute  the  predicate,  while  affir- 
mative propositions  do  not. 

8.  State  precisely  what  is  asserted  by  Proposition  I.     What 
forms   may   the   diagrams   which   represent    this   proposition 
assume  ? 

CHAPTER  VII.  —  The  Interpretation  of  Propositions 

1.  Why  is  it  better  to  speak  of  the  Interpretation  of  propo- 
sitions than  to  use  the  term  '  Immediate  Inference  '  ? 

2.  What  is  meant  by  the  Opposition  of  propositions? 

3.  Explain  the  distinction  between  Contrary  and  Contradic- 
tory propositions. 

4.  If  proposition  O  is  false,  what  is  known  regarding  the 
truth  or  falsity  of  A,  E,  and  I  ? 


QUESTIONS   AND   EXERCISES  355 

5.  What  is  the  simplest  proposition  which  must  be  estab- 
lished in  order  to  disprove  the  following  statements  :   (a)  All 
men  desire  wealth.     (^)  No  man  is  perfectly  happy.     (c)  Some 
knowledge  is  not  of  any  value,     (d)  Pain  alone  is  evil,     (e)  All 
is  not  lost. 

6.  Give  the  contrary  (or  sub-contrary) ,  and  the  contradictory 
of:   (a)  All  metals  are  elements,     (b)  No  coward  need  apply. 
(<r)  Socrates  was  the  wisest  man  in  Athens,     (d)  Not  all  men 
are  brave,     (e)  No  man  but  a  traitor  would  have  done  this. 

7.  Give  the  Obverse  of  the  following  propositions  :  — 

(1)  All  horses  are  quadrupeds. 

(2)  Good  men  are  charitable. 

(3)  None  of  the  captives  escaped. 

(4)  Some  of  the  planets  are  not  larger  than  the  earth. 

(5)  Some  students  do  not  fail  in  anything. 

(6)  All  English  dukes  are  members  of  the  House  of  Lords. 

(7)  No  illogical  author  is  truly  scientific. 

8.  Convert  in  at  least  one  way  :  — 
(T)  All  men  are  rational. 

(2)  Some  metals  are  readily  fusible. 

(3)  Perfect  happiness  is  impossible. 

(4)  None  of  the  captives  escaped. 

(5)  Uneasy  lies  the  head  that  wears  a  crown. 

(6)  Not  every  man  could  stand  such  hardships. 

(7)  None  but  the  brave  deserves  the  fair. 

(8)  Phosphorus  will  not  dissolve  in  alcohol. 

(9)  Hydrogen  is  the  lightest  body  known. 
(10)  The  world  is  my  idea. 

9.  Convert  by  contraposition  :  — 

(1)  All  honest  men  are  of  this  opinion. 

(2)  Oxygen  can  be  prepared  by  heating  potassium  chlo- 

rate in  a  thin  glass  flask, 


356  QUESTIONS   AND   EXERCISES 

(3)  Some  of  the  enemy  were  not  prepared  to  surrender. 

(4)  Not  all  who  came  to  scoff  remained  to  pray. 

(5)  A  triangle  is  a  plane  figure  bounded  by  three  straight 

lines. 

(6)  The  return  of  peace  had  given  fresh  confidence  to 

the  government  party. 

10.  Describe  the  logical  relation  between  each  of  the  four 
following  propositions :  — 

(1)  All  substances  which  are  material  possess  gravity. 

(2)  No  substances  which  possess  gravity  are  immaterial. 

(3)  Some  substances  which  are  immaterial  do  not  possess 

gravity. 

(4)  Some  substances  which  do  not  possess  gravity  are 

immaterial.     (Jevons.) 

11.  What  is  the  Obverse  of  the  Converse  of,  'None  of  the 
planets  shine  by  their  own  light '  ? 

12.  Can  we  logically  conclude  that  because  heat  expands 
bodies,  therefore  cold  contracts  them?     (Jevons.) 

13.  What  is  the  logical  relation,  if  any,  between  the  two 
assertions  in  Proverbs  xi.  i,  '  A  false  balance  is  an  abomination 
to  the  Lord ;  but  a  just  weight  is  his  delight '  ?     (Jevons.) 

CHAPTER  VIII.  —  The  Syllogism  and  its  Rules 

1.  What  is  the  relation  of  the  Proposition  and  the  Syllo- 
gism? 

2.  What  is  the  function  of  the  Middle  Term  in  a  Syllogism? 

3.  How  are  the  major  and  minor  terms,  and  the  major  and 
minor  premises  of  a  Syllogism  distinguished  ? 

4.  Prove  the  seventh  and  eighth  canon  of  the  Syllogism, 
(a)   by  means  of  the  previous  rules,  and  (b)  by  the  use  of 
circles. 


QUESTIONS  AND   EXERCISES  357 

5 .  Construct  an  argument  to  illustrate  the  fallacy  of  ambigu- 
ous middle  term. 

6.  Arrange  the  following  arguments  in  the  regular  logical 
order  of  major  premise,  minor  premise,  and  conclusion,  and 
examine  them  to  see  whether  they  conform  to  the  canons  of 
the  Syllogism :  — 

(1)  Gold  is  not  a  compound  substance  ;  for  it  is  a  metal, 

and  none  of  the  metals  are  compounds. 

(2)  All  national  holidays  are  bank  holidays,  the  bank  will 

therefore  be  closed  on  the  fourth  of  July. 

(3)  All    cruel    men   are   cowards,   no   college   men   are 

cruel,  therefore  no  college  men  are  cowards. 

(4)  Some  useful  metals  are  becoming  rarer.     Iron  is  a 

useful  metal,  and  is  therefore  becoming  rarer. 

(5)  This  man  shares  his  money  with  the  poor,  but  no 

thief  ever  does  this,  therefore  this  man  is  not  a 
thief. 

(6)  He  who  is  content  with  what  he  has  is  truly  rich. 

An  envious  man  is  not  content  with  what  he  has ; 
no  envious  man  therefore  is  truly  rich. 

7.  What  does  the  Figure  of  an  Argument  depend  upon? 
How  do  you  distinguish  the  four  figures? 

CHAPTER  IX.  —  The  Valid  Moods  and  the  Reduction  of  Figures 

1.  Arrange  the  following  arguments  in  logical  order,  and 
give  the  mood  and  figure  in  each  case :  — 

(i)  No  P  is  M,  (2)  All  M  is  S, 

Some  S  is  M,  Some  M  is  P, 

Therefore  some  S  is  not  P.  Therefore  some  S  is  P. 

2.  Name  the  premises  from  which  valid  conclusions  may 
be  drawn,  no  account  being  taken  of  figures  :  — 


358  QUESTIONS   AND   EXERCISES 

AA,     EO,      IA,      IO,      II,      EE,      El,     AE,     EA,     OO. 

3.  Prove  the  special  canons  of  the  fourth  figure. 

4.  'The  middle  term  must  be  distributed  once  at  least.' 
In  what  figures  may  it  be  distributed   twice?    What  is  the 
character  of  the  conclusion  when  this  occurs? 

5.  Prove  generally  that  when  the  major  term  is  predicate  in 
its  premise,  the  minor  premise  must  be  affirmative. 

6.  If  the  major  term  be  distributed  in  its  premise,  but  used 
undistributively  in  the  conclusion,  determine  the  mood  and 
figure. 

7.  Explain  why  we  can  obtain  only  negative  conclusions  by 
means  of  the  second  figure  and  particular  conclusions  by  means 
of  the  third  figure. 

8.  What  conclusions  do  AA,  AE,  and  EA  yield  in  the  fourth 
figure  ?     Explain. 

9.  Is  it  possible  for  both  major  and  minor  terms  to  be  par- 
ticular at  the  same  time  in  the  premises  ?     If  so,  construct  an 
argument  where  this  is  the  case. 

10.  What  do  you  understand  by  Reduction?    Reduce  the 
following  argument  to  the  first  figure  :  — 

No  fixed  stars  are  planets, 

All  planets  are  bright  and  shining, 

Therefore  some  bright  and  shining  bodies  are  not  fixed  stars. 

CHAPTER  X.  —  Abbreviated  and  Irregular  Arguments 

i.  Complete  the  following  arguments,  determine  their  mood 
and  figure,  and  examine  them  to  see  if  they  violate  any  of  the 
rules  of  the  syllogism  :  — 

(i)    Blessed  are   the   meek,   for  they  shall   inherit   the 

earth. 
'2)    He  must  be  a  strong  man,  for  he  was  on  the  crew. 


0 


QUESTIONS  AND   EXERCISES  359 

(3)  Zoophytes  have  no  flowers ;  therefore  they  are  not 

plants. 

(4)  None  but  material  bodies  gravitate,  therefore  air  is 

a  material  body. 

(5)  He  has  been  a  politician  for  years,  and  is  therefore 

not  to  be  trusted. 

2.  Illustrate   the   difference    between    the    Progressive  or 
Synthetic,  and   the   Regressive   or  Analytic   methods  as  em- 
ployed   in   Mathematics    and    Psychology.      May   a   science 
employ  both  methods  at  the  same  time  ? 

3.  Break  up  the   concrete   examples  of  Sorites  given   on 
pages  130,  131,  into  syllogisms. 

4.  Show  generally  why  all  the  premises  except  the  first  in 
the  Aristotelian  Sorites  must  be  universal. 

5.  Prove  that  in  the  Goclenian  Sorites  the   first   premise 
alone  can  be -negative,  and  the  last  alone  particular. 

6.  In  the  examples  of  arguments  given  on  page  133,  is  there 
any  middle  term?     If  not,  what  serves  as  the  standard  of 
comparison  ? 

CHAPTER  XL  —  Hypothetical  and  Disjunctive  Arguments 

1.  What   reasons   are  there  for  classifying  the  disjunctive 
proposition  as  conditional  ? 

2.  What  are  the  rules  of  the  hypothetical  syllogism  ? 

3.  Is  it  ever  possible  to  obtain  a  valid  conclusion  by  deny- 
ing the  antecedent  or  affirming  the  consequent  ? 

4.  Determine  which  of  the  following  hypothetical  arguments 
are  valid    and  which  invalid;   then  express  the  latter  in  the 
categorical  form,  pointing  out  what  are  the  categorical  fallacies 
which  result :  — 

(i)    If  a  man  is  avaricious,  he  will  be  unhappy ;  but  A  is 


360  QUESTIONS  AND    EXERCISES 

unhappy,  and  we  may  therefore  conclude  that  he  is 
avaricious. 

(2)  If  A  is  B,  C  is  D,  but  A  is  B,  therefore  we  may 

conclude  that  C  is  D. 

(3)  If  the  door  were  locked,  the  horse  would  not  be 

stolen  ;  but  the  horse  is  not  stolen,  therefore  the 
door  must  have  been  locked. 

(4)  If  man  were  not  capable  of  progress,  he  would  not 

differ  from  the  brutes ;  but  man  does  differ  from 
the  brutes,  therefore  he  is  capable  of  progress. 

(5)  If  he  had  studied  his  lesson,  he  would  have  been 

able  to  recite  ;  but  he  was  able  to  recite,  and  there- 
fore must  have  studied  his  lesson. 

(6)  If  it  becomes  colder  to-night,  the  pond  will  be  frozen 

over;    but   it   will    not   become    colder    to-night, 
therefore  the  pond  will  not  be  frozen  over. 

5.  What  aspects  of  thinking  are  emphasized  by  the  cate- 
gorical and  hypothetical  forms  of  reasoning  respectively? 

6.  How  far  may  the  disjunctive  proposition  be  regarded  as 
an  expression  of  ignorance,  and  what  is  the  justification   for 
the  statement  that  it  involves  systematic  knowledge? 

7.  To  what  fallacy  is   the   disjunctive   argument   specially 
liable? 

8.  How  would  you  criticise  the  dilemmatic  arguments  given 
on  page  150? 

CHAPTER  XII.  —  Fallacies  of  Deductive  Reasoning 

1.  What  is  the  distinction  between  errors  of  interpretation 
and  fallacies  in  reasoning? 

2.  Why  is  the  detection  of  material  fallacies  a  proper  subject 
of  logic? 

3.  If  it  is  true  that  all  the  righteous  people  are  happy,  can 


QUESTIONS  AND   EXERCISES  361 

we  conclude  that  all  unhappy  people  are  unrighteous  ?      If  so, 
how  do  we  pass  from  the  first  statement  to  the  second? 

4.  Can  we  proceed  logically  from  the  proposition,  '  all  good 
citizens  vote  at  elections/  to  'all  who  vote  in  elections  are 
good  citizens  '  ? 

5.  Does  the  statement  that  '  some  sciences  are  useful/  justify 
the  proposition  that  '  some  useful  things  are  not  sciences '  ? 

6.  Mention  the  fallacies  of  Equivocation,  and  explain  what  is 
common  to  them  all. 

7.  Explain  the  terms  :  Petitio  Principii,  Circulus  inprobando, 
Argumentum  ad  hominem,  Argumentum  ad populum. 

8.  Examine  the  following  reasoning :    '  The  argument  from 
design  must  be  regarded  as  without  value ;    for  it  has  been  re- 
jected by  Spinoza,  Kant,  Spencer,  and  Darwin.' 

MISCELLANEOUS  EXAMPLES 

Arrange  the  following  arguments  whenever  possible  in  regular 
logical  order ;  determine  whether  or  not  they  are  valid ;  give 
the  mood  and  figure  of  the  valid  categorical  arguments  ;  if  any 
argument  is  invalid,  point  out  and  name  the  fallacy  involved  :  — 

1.  All  virtue  is  praiseworthy,  and  charity  is  a  virtue,  there- 
fore charity  is  praiseworthy. 

2.  All  colours  are  physical  phenomena;  but  no  sound  is  a 
a  colour,  therefore  no  sound  is  a  physical  phenomenon. 

3.  Some  minerals  are  precious  stones,  all  topazes  are  pre- 
cious stones,  therefore  some  minerals  are  topazes. 

4.  Some   acts   of  homicide   are   laudable,    therefore  some 
cruel  things  are  laudable. 

5 .  If  he  has  found  the  treasure,  he  is  rich ;    but  he  has  not 
found  it,  therefore  he  is  not  rich. 

6.  He  must  be  a  Democrat ;  for  all  the  Democrats  believe 
in  Free  Trade. 


362  QUESTIONS  AND   EXERCISES 

7.  If  only  the  ignorant  despise  knowledge,  this  man  cannot 
be  ignorant,  for  he  praises  it.     (Edinburgh,  1892.) 

8.  Whatever  is  given  on  the  evidence  of  sense  may  be  taken 
as  a  fact ;  the  existence  of  God,  therefore,  is  not  a  fact,  for  it  is 
not  evident  to  sense.     (St.  Andrews,  1896.) 

9.  This  explosion  must  have  been  occasioned  by  gunpowder ; 
for  nothing  else  would  have  possessed  sufficient  force. 

10.  This   burglary  is,  the  work   of  a   professional;    for  an 
amateur  would  not  have  been  half  so  clever. 

11.  No  stupid  person  can  become  President  of  the  United 
States ;  therefore  Mr.  Cleveland  and  Mr.  McKinley  must  both 
be  men  of  ability. 

12.  Since  almost  all  the  organs  of  the  body  have  some  use, 
the  vermiform  appendix  must  be  useful. 

13.  Every  candid  man  acknowledges  merit  in  a  rival,  every 
learned  man  does  not  do  so ;  therefore  learned  men  are  not 
candid. 

14.  Every  book  is  liable  to  error,  every  book  is  a  human 
production,  therefore  all  human  productions  are  liable  to  error. 

15.  Learned  men  sometimes  become  mad;  but  as  he  is  not 
learned,  there  is  no  danger  of  his  sanity. 

1 6.  If  this  candidate  used  money  to  secure  his  election,  he 
deserved  defeat ;    but  he  did  not  use  money  in  this  way,  and 
therefore  did  not  deserve  defeat. 

1 7.  All  valid  syllogisms  have  three  terms ;  this  syllogism  is 
therefore  valid,  for  it  has  three  terms. 

1 8.  No  persons  destitute  of  imagination  are   true   poets; 
some  persons  destitute   of  imagination  are  good   reasoners; 
therefore  some  good  reasoners  are  not  true  poets. 

19.  Only  material  bodies  gravitate  ;  ether  does  not  gravitate. 

20.  In  reply  to  the  gentleman's  arguments,  I  need  only  say 
that  two  years  ago  he  advocated  the  very  measure  which  he 
now  opposes. 


QUESTIONS  AND    EXERCISES  363 

21.  If  he  claims  that  he  did  not  steal  the  goods,  why,  I  ask, 
did  he  hide  them  as  no  thief  ever  fails  to  do  ? 

22.  If  this  therefore  be  absurd  in  fact  and  theory,  it  must 
also  be  absurd  in  idea,  since  nothing  of  which  we  can  form  a 
clear  and  distinct  idea  is  impossible.      (Hume,  Treatise  of 
Human  Nature.) 

23.  Whatever  is  produced  without  a  cause  is  produced  by 
nothing,  or  in  other  words  has  nothing   for  its  cause.     But 
nothing  can  never  be  a  cause.     Hence  every  object  has  a  real 
cause  of  its  existence.     (Hume,  Treatise) 

24.  Everything  must  have  a  cause ;  for  if  anything  wanted 
a  cause  it  would  produce  itself,  that  is,  exist  before  it  existed, 
which  is  impossible.     (Hume,  Treatise) 

25.  If  it   be   true,  as   Mr.  Spencer   thinks,  that   the   past 
experience  of  the  race  has  produced  innate   ideas  and  feel- 
ings, Weismann's  denial  of  Use-inheritance  would  be  refuted. 
Certainly,  but  it  is  just  possible  that  Mr.  Spencer's  theory  is 
not  true. 

26.  Democracy  is  not  a  perfect  form  of  government,  for 
under  it  there  are  able  men  who  do  not  get  power;  and  so 
it  allows  men  to  get  power  who  are  not  able. 

27.  Of  university  professors,  some  are  zealous  investigators, 
and  some  good  teachers.     A  is  an  excellent  teacher,  and  we 
may  therefore  conclude  that  he  is  not  a  zealous  investigator. 

28.  Seeing  that  abundance  of  work  is  a  sure  sign  of  indus- 
trial prosperity,  it  follows  that  fire  and  hurricane  benefit  in- 
dustry, because  they  undoubtedly  create  work.     (St.  Andrews, 

1895.) 

29.  I  will  have  no  more  doctors  ;  I  see  that  all  of  those  who 
have  died  this  winter  have  had  doctors.     (St.  Andrews,  1896.) 

30.  If  a  man  is  educated,  he  does  not  want  to  work  with  his 
hands;   consequently,  if  education  is  universal,  industry  will 
cease.     (London,  1897.) 


364  QUESTIONS   AND   EXERCISES 

31.  None  but  the  wise  are  good,  and  none  but  the  good  are 
happy,  therefore  none  but  the  wise  are  happy.     (Edinburgh, 
1897.) 

32.  Giving  advice  is  useless.     For  either  you  advise  a  man 
what  he  means  to  do,  in  which  case  the  advice  is  superfluous  ; 
or  you  advise  him  what  he  does  not  mean  to  do,  and  the  advice 
is  ineffectual.     (London,  1897.) 

33.  No  pauper  has  a  vote,  A  B  is  not  a  pauper,  therefore 
he  has  a  vote.     (St.  Andrews,  1897.) 

34.  The  love  of  nature  is  never  found  either  in  the  stupid 
or  the  immoral  man,  therefore  stupidity  and  virtue  are  incom- 
patible.    (Edinburgh,  1897.) 

35.  Not  all  educated  persons  spell  correctly;  for  one  often 
finds  mistakes  in  the  papers  of  University  students. 

36.  Free  Trade  is  a  great  boon  to  the  workirfgman ;  for  it 
increases  trade,  and  -this  cheapens  articles  of  ordinary  con- 
sumption; this   gives  a  greater  purchasing  power  to  money, 
which  is  equivalent  to  a  rise   in  real  wages,  and  any  rise  in 
real  wages  is  a  boon  to  the  workingman. 

37.  If  the  train  is  late,  I  shall  miss  my  appointment ;  if  it  is 
not  late,  I  shall  not  reach  the  depot  in  time  to  go  by  it,  there- 
fore, in  any  case,  I  shall  miss  my  appointment. 

38.  He  who  spareth  the  rod  hateth  his  child;  the  parent 
who  loves  his  child  therefore  spareth  not  the  rod. 

39.  Whatever  tends  to  withdraw  the  mind  from  pursuits  of 
a  low  nature  deserves  to  be  promoted ;  classical  learning  does 
this,  since  it  gives  us  a  taste  for  intellectual  enjoyments ;  there- 
fore it  deserves  to  be  promoted. 

40.  As  against  the  proposition  that  the  formation  of  public 
libraries  prevents  private  individuals  from  purchasing,  and  so 
decreases   the   sale   of  books,  a   writer  urges   that  whatever 
encourages  the  reading   of  books  encourages  the  buying  of 
books.     It  is  a  library's  purpose  to  encourage  reading,  and 


QUESTIONS  AND   EXERCISES  365 

hence  the  net  result  is  rather  to  increase  than  to  lessen  pur- 
chases. 

41.  No  reason  however  can  be  given  why  the  general  hap- 
piness is  desirable,  except   that   each   person,  so  far  as   he 
believes  it  to  be  attainable,  desires  his  own  happiness.     This, 
however,  being  a  fact,  we  have  not  only  all  the  proof  which 
the  case  admits  of,  but  all  which  it  is  possible  to  require,  that 
happiness  is  a  good,  that  each  person's  happiness  is  a  good  to 
that  person,  and  the  general  happiness,  therefore,  a  good  to 
the  aggregate  of  all  persons.     (Mill's  Utilitarianism.) 

42.  This  man  is  a  Protestant;  for  he  exercises  the  right  of 
private  judgment. 

43.  If  the  orbit  of  a  comet  is  diminished,  either  the  comet 
passes  through  a  resisting  medium,  or  the  law  of  gravitation  is 
partially  suspended.     But  the'  second  alternative  is  inadmis- 
sible.    Hence  if  the  orbit  of  a  comet  is  diminished,  there  is 
present  a  resisting  medium. 

44.  How  do  we  know  that  our  intuitive  beliefs  concerning 
the  world  are  invariably  true?     Either  it  must  be  from  experi- 
ence establishing  the  harmony,  or  an  intuitive  belief  must  certify 
the  correctness.      Now  experience  cannot  warrant  such  har- 
mony except  in  so  far  as  it  has  been  perceived.     Still  more 
futile  is  it  to  make  one  instinctive  belief  the  cause  of  another. 
Thus  we  cannot  know  that  any  intuitive  belief  is  universally 
valid.     (Bain.) 

45.  Which  of  the  following  are  real  inferences  :     (i)   'This 
weighs  that  down,  therefore  it  is  heavier' ;   (2)  'This  piece  of 
marble  is  larger  than  that,  and  therefore  is  heavier.' 

46.  The  parts  of  pure  space  are  immovable,  which  follows 
from  their  inseparability,  motion  being  nothing  but  change  of 
distance  between  any  two  things  ;  but  this  cannot  be  between 
parts  that  are  inseparable,  which  therefore  must  be  at  per- 
petual rest  one  amongst  another. 


366  QUESTIONS  AND   EXERCISES 

47.  If  a  body  moves,  it  must  move  either  in  the  place  where 
it  is,  or  in  the  place  where  it  is  not.     But  a  body  cannot  move 
in  the  place  where  it  is,  nor  yet  in  the  place  where  it  is  not. 
Hence  a  body  cannot  move  at  all. 

48.  We  have  no  perfect  idea  of  anything  but  a  perception. 
A  substance  is  entirely  different  from  a  perception.     We  have 
therefore  no  idea  of  substance.     (Hume.) 

49.  Every  good  government  promotes  the  intelligence  of  the 
people,  and  no  despotism  does  that.     (Bain.) 

50.  He  was  too  impulsive  a  man  not  to  have  committed 
many  errors.     (Bain.) 

51.  A  true  philosopher  is  independent  of  the  caprices  of 
fortune,  for  he  places  his  chief  happiness  in  moral  and  intel- 
lectual excellence. 

52.  Educated  among  savages,  he  could  not  be  expected  to 
know  the  customs  of  polite  society.     (Bain.) 

53.  No  war  is  long  popular;  for  every  war  increases  taxa- 
tion, and  the  popularity  of  anything  that  touches  our  pockets 
is  very  short  lived. 

54.  The  general  object  which  all   laws  have,  or-  ought   to 
have,  in  common,  is  to  augment  the  total  happiness  of  the 
community ;  and  therefore,  in  the  first  place,  to  exclude  as  far 
as  may  be  everything  that  tends  to  subtract  from  that  happi- 
ness :  in  other  words,  to  exclude  mischief.    But  all  punishment 
is  mischief;  all  punishment  in  itself  is  evil.     Upon  the  princi- 
ple of  utility,  if  it  ought  at  all  to  be  admitted,  it  ought  only  to 
be  admitted  in  as  far  as  it  promises  to  exclude  some  greater 
evil.     (Bentham.) 

55.  Experiments  for  the  purpose  of  ascertaining  the  func- 
tions of  the  various  brgans  in  animals  cause  pain,  and  as  we  are 
not  warranted  in  causing  pain  to  any  sentient  creature,  such 
experiments  are  wrong. 

56.  Thou  shalt  not  bear  false  witness  against  thy  neighbour. 


QUESTIONS  AND   EXERCISES  367 

57.  What  is  the  use  of  all  this  teaching?     Every  day  you 
hear  of  a  fraud  or  forgery,  by  some  one  who  might  have  led 
an  innocent  life,  if  he  had  never  learned  to  read  and  write. 
(Edinburgh.) 

58.  Pious  men  only  are  fit  to  be  ministers  of  religion ;  some 
men  who  have  not  received  a  college  education  are  pious  men, 
therefore  such  men  are  fitted  to  be  ministers  of  religion. 

59.  What  fallacy  did  Columbus  commit  when  he  proved 
that  an  egg  could  stand  on  end?    (Jevons.) 

60.  No  traitor  is  to  be  trusted,   John  is   no  traitor,  and 
therefore  is  to  be  trusted. 

6 1 .  Against  what  fallacy  does  the  proverb,  '  all  that  glitters 
is  not  gold,'  warn  us  ? 

62.  Livy  describes  prodigies  in  his  history,  therefore  he  is 
never  to  be  believed. 

63.  The  theory  of  evolution  is  true,  for  it  is  accepted  by 
every  scientific  biologist. 

64.  The  theory  of  evolution  is  not  true,  for  it  was  not  ac- 
cepted by  Agassiz,  nor  by  Gladstone ;  moreover,  you  cannot 
accept  this  doctrine,  for  it  is  disclaimed  by  the  authorities  of 
your  church. 

65.  The  advantages  which  would  accrue  to  the  working- 
classes  are  not  sufficient  to  justify  Protection,  neither  are  the 
advantages  which  it  would  bring  to  the  farmers  or  the  manu- 
facturers, or  to  any  other  class  in  the  community ;  Protection 
therefore  has  not  enough  advantages  to  justify  it. 

66.  No  man  should  be  punished  if  he  is  innocent;  this  man 
should  not  be  punished ;  therefore  he  is  innocent. 

67.  He  could  not  face  bullets  on  the  field  of  battle,  and  is 
therefore  a  coward. 

68.  We  know  that  God  exists  because  the  Bible  tells  us  so ; 
and  we  know  that  whatever  the  Bible  affirms  must  be  true 
because  it  is  of  divine  origin. 


368  QUESTIONS  AND   EXERCISES 

69.  Nations  are  justified  in  revolting  when  badly  governed; 
for  every  people  has  a  right  to  good  government.   (Edinburgh.) 

70.  When  Croesus  was  about  to  make  war  upon  Cyrus,  King 
of  Persia,  he  consulted  the  oracle  at  Delphi,  and  received  for 
an  answer  that,  if  he  should  wage  war  against  the  Persians,  he 
would  overthrow  a  mighty  empire. 

71.  England  has  a  gold  coinage,  and  is  a  very  wealthy  coun- 
try, therefore  it  may  be  inferred  that  other  countries  having  a 
gold  coinage  will  be  wealthy. 

72.  Your  arguments  against  the  philosophy  of  Hegel  are 
of  no  value ;  for  you  uphold  that  of  Schopenhauer,  which  is 
equally  repugnant  to  common  sense. 

73.  For  those  who  are  bent  on  cultivating  their  minds  by 
diligent  study,  the  incitement  of  academical  honours  is  unnec- 
essary ;  and  it  is  ineffectual  for  the  idle,  and  such  as  are  in- 
different to  mental  improvement ;  therefore  the  incitement  of 
academical  honours  is  either  unnecessary  or  ineffectual. 

74.  Without  order  there  is  no  living  in  public  society,  be- 
cause the  want  thereof  is  the  mother  of  confusion,  whereupon 
division  of  necessity  followeth ;  and  out  of  division,  destruction. 

75.  If  it  is  always  impossible  not  to  sin,  it  is  always  unjust  to 
punish.     Now  it  is  always  impossible  not  to  sin,  for  all  that  is 
predetermined  is  necessary,  and  all  that  is   foreseen  is  pre- 
determined, and  every  event  is  foreseen.     Hence  it  is  always 
unjust  to  punish.     (Leibniz,  Theodicy^) 

76.  If  a  gas  is  heated,  its  temperature  rises ;  if  its  tempera- 
ture rises,  its  elastic  force  increases  ;  if  its  elastic  force  increases, 
the  pressure  on  the  walls  of  the  containing  vessel  increases ; 
therefore  if  a  gas  is  heated,  the  pressure  on  the  walls  of  the 
containing  vessel  increases.     (Ray.) 

77.  The  end  of  human  life  is  either  perfection  or  happi- 
ness ;  death  is  the  end  of  human  life,  therefore  death  is  either 
perfection  or  happiness. 


QUESTIONS   AND   EXERCISES  369 

78.  If  light  consisted  of  material  particles,  it  would  possess 
momentum ;  it  cannot  consist  of  material  particles,  for  it  does 
not  possess  momentum. 

79.  This  person  is  very  learned,  and  very  sociable,  hence  it 
follows  that  learning  increases  sociability. 

80.  Why  advocate  socialism?     Until  men  become  morally 
perfect,  it  is  impossible ;  when  they  have  become  so,  it  will  be 
unnecessary.     (Edinburgh.) 

8 1.  The  diameter  of  the  earth  is,  in  round  numbers,  forty 
millions  of  feet.     Consequently  the  attraction  of  a  sphere  of  the 
same  mean  density  as  the  earth,  but  one  foot  in  diameter,  will 
be  TroWfr  Part  the  attraction  of  the  earth ;  that  is,  TTnrJinnnr 
of  the  weight  of  the  body  attracted.     Consequently,  if  we  should 
measure  the  attraction  of  such  a  sphere  of  lead,  and  find  that 
it  was  just  YffinAnnnr  tnat  °f  tne  weight  of  the  body  attracted, 
we  would  conclude  that  the  mean  density  of  the  earth  was 
equal  to  that  of  lead.     But  the  attraction  is  actually  found  to 
be  nearly  twice  as  great  as  this  ;  consequently  a  leaden  sphere 
is  nearly  twice  as  dense  as  the  average  of  the  matter  composing 
the  earth.     (Newcomb,  Popular  Astronomy.) 

82.  Mr.  C.  said  that  he  was  certain  that  the  donors  gave  the 
pioperty   to    the   institution   with    a   distinct   and   unanimous 
understanding  as  to  its  future  use.     The  directors  who  acted 
for  the  institution  in  this  transfer  must  necessarily  have  had  an 
understanding,  either  the  same  as  that  of  the  donors,  or  differ- 
ent.    If  the  understanding  of  the  directors  was  the  same  as 
that  of  the  donors,  then  they,  the  former,  were  unquestionably 
bound  to  live  up  to  that  understanding.     If  it  was  different, 
then  the  property  was  conveyed  on  a  misunderstanding,  and 
every  dictate  of  honour  and  fair  play  would  demand  the  return 
of  the  property. 

2B 


370  QUESTIONS  AND   EXERCISES 

PART  II.  —  INDUCTIVE  METHODS 
CHAPTER  XIII.  —  The  Problem  of  Induction 

1.  Explain  why  syllogistic  logic  is  not  a  complete  account 
of  the  nature  of  thinking. 

2.  In  what  sense  is  it  possible  to  lay  down  the  laws  of  scien- 
tific procedure  ? 

3.  In  solving  a  complex  scientific  problem  do  we  usually 
employ  but  a  single  method  ? 

4.  What  can  you  say  regarding  the  division  of  inductive 
methods  into  methods  of  Observation,  and  methods  of  Expla- 
nation ? 

5.  Would  it  be  permissible  to  add  Experimental  methods  as 
a  third  and  independent  class  ? 

6.  What  is  the  distinction  between  '  empirical '  and  '  scien- 
tific '  knowledge  ? 

7.  What  are  the  advantages  to  be  derived  from  experiments 
in  scientific  work  ? 

CHAPTER  XIV.  —  Enumeration  and  Statistics 

1.  What  is  the  justification  for  beginning  our  account  of  the 
inductive  methods  with  Enumeration? 

2.  Explain   what    Jevons   regards   as   'Perfect'   induction. 
Has  this  process  any  right  to  the  name? 

3.  For  what  purpose  are  statistics   employed?     To  what 
classes  of  phenomena  are  they  applied? 

4.  What  is  meant  by  a  phenomenon? 

5.  Explain  how  statistics  may  suggest  causal  laws,  or  confirm 
our  expectation  of  them.     May  statistics  also  be  used  to  dis- 
prove a  proposed  law  of  causal  connection?     Illustrate  your 
answer. 


QUESTIONS   AND   EXERCISES  371 

6.  Explain  what  is  meant  by  the  *  average,'  and  show  how  it 
is  obtained. 

7.  How  does  the  procedure  of  insurance  companies  differ 
from  gambling? 

CHAPTER  XV.  —  Causal  Determination 

1.  What  are  the  two  main  principles  upon  which  the  canons 
proposed  by  Mill  are  founded  ? 

2.  Give  the  Canon  of  the  Method  of  Agreement,  and  illus- 
trate its  use. 

3.  'I  have  noticed  that  A  always  precedes  B,  it  is  there- 
fore the  cause  of  B.'     Is  this  good  reasoning? 

4.  What  is  meant  by  the  '  Plurality  of  Causes  '  ? 

5 .  Under  what  disadvantages  does  the  Method  of  Agreement 
labour?     How  is  it  supplemented? 

6.  State  and  illustrate  the  canon  of  the  Method  of  Differ- 
ence. 

7.  Why  is  this  method  applicable  only  to  the  spheres  where 
experiment  can  be  employed?     Would  it  be  safe  to  depend 
upon  this  method  in  determining  the  causes  of  social  or  politi- 
cal conditions? 

CHAPTER  XVI.  —  Causal  Determination  {continued) 

1.  Where  do  we  employ  the  Joint  Method? 

2.  What  would   it   be  necessary  to   establish   in  order  to 
prove   inductively  that   some  change   in   the   tariff  laws   was 
beneficial  to  the  country? 

3.  ( One  of  the  main  characteristics  of  modern  science  is  its 
quantitative  nature.'     Explain. 

4.  How  does  the  law  of  Concomitant  Variations  assist  us  in 
determining  causal  relations? 


3/2  QUESTIONS   AND   EXERCISES 

5.  In  what   two   ways   may   the  Method  of  Residues   be 
applied  ? 

6.  Mention  some  discoveries  to  which  the  investigation  of 
unexplained  residues  has  led. 

CHAPTER  XVII.  —  Analogy 

1.  Why  do  we  include  Analogy  among  the  methods  of  Ex- 
planation ? 

2.  What  do  you  mean  by  Analogy?     What  is  the  principle 
upon  which  it  proceeds  ? 

3.  How  is  the  word  used  in  mathematical  reasoning,  and  in 
physiology  ? 

4.  Into  what  Figure  of  the  Syllogism  does  an  argument 
from  Analogy  naturally  fall?     Is  the  argument  formally  valid, 
and 'if  not,  to  what  syllogistic  fallacy  does  it  correspond? 

5.  Explain  how  Analogy  may  suggest  a  true  law  or  explana- 
tory principle. 

6.  Why  do  we  speak  of  Analogy  as  Incomplete  Explanation  ? 

7.  If  all  analogical  reasoning  yields  only  probability,  is  not 
one  analogy  as  good  as  another  for  purposes  of  inference  ?     If 
not,  upon  what  does  the  value  of  an  inference  from  Analogy 
depend  ? 

CHAPTER  XVIII.  —  The  Use  of  Hypotheses 

1 .  How  do  you  distinguish  the  terms   '  theory '  and  '  hy- 
pothesis '  ? 

2.  What  is  an  hypothesis,  and  how  is  it  used? 

3.  Do   hypotheses  play  any  part  in  assisting  Observation? 
Explain  and  illustrate. 

4.  Give  some  instances  in  which  hypotheses  have  proved 
injurious,  and  have   misled  people   regarding   the   nature  of 
facts. 


QUESTIONS   AND    EXERCISES  373 

5.  'Hypotheses  are  formed  by  the  imagination  working  in 
dependence  upon  facts  and  guided  by  analogy.'     Explain. 

6.  What  are  the  steps  in  the  proof  of  an  hypothesis? 

7.  Explain  what  part  is  played  by  Induction  and  Deduction 
respectively  in  using  hypotheses. 

8.  What  canons  have  been  laid  down  to  which  a  good  hy- 
pothesis must  conform  ?     Why  are  the  first  and  third  of  these 
rules  of  little  value  ? 

9.  Explain  why  an  unverifiable  hypothesis  is  not  worth  dis- 
cussing. 

CHAPTER  XIX.  —  Fallacies  of  Induction 

1 .  What  is  the  source  of  fallacy  ?    How  far  is  it  true  that  the 
study  of  Logic  can  protect  us  from  fallacies  ? 

2.  How  do  you  classify  Inductive  Fallacies? 

3.  Explain  and  illustrate  the  following  fallacies :    Question- 
begging  Epithet,  Equivocation,  Fallacies  due  to  Figurative  Lan- 
guage. 

4.  Explain  and  illustrate  the  tendency  of  the  mind  to  neg- 
lect negative  cases. 

5 .  Is  it  an  easy  matter  to  '  tell  just  what  we  saw  and  heard ' 
at  a  particular  time  ? 

6.  What  do  you  mean  by  post  hoc  ergo  propter  hoc  ?     Why 
may  we  take  this  as  the  general  type  of  inductive  fallacies  ? 

7.  What  did  Bacon  mean  by  the  Idols  of  the  Cave? 

8.  '  Every  age,  as  well  as  every  individual,  has  its  idols.' 
Explain  this   statement. 

MISCELLANEOUS  EXAMPLES 

Analyze  the  examples  of  inductive  reasoning  given  below, 
and  point  out  what  methods  are  employed,  indicating  also 
whether  or  not  the  conclusion  is  completely  established :  — 


3/4  QUESTIONS  AND   EXERCISES 

1.  In  my  experience  A  has  been  invariably  preceded  by  B, 
and  we  may  therefore  conclude  that  it  is  the  cause  of  it. 

2.  Scarlet  poppies,  scarlet  verbenas,  the  scarlet  hawthorn, 
and  honeysuckle  are  all  odourless,  therefore  we  may  conclude 
that  all  scarlet  flowers  are  destitute  of  odour. 

3.  What  inference,  if  any,  can  be  drawn  from  the  follow- 
ing statement :    '  In  nine  counties,  in  which   the   population 
is   from    100   to    150   per   square   mile,   the   births   are    296 
to    100   marriages;    in   sixteen   counties,   with   a   population 
of  150  to  200  per  square  mile,  the  births  are  308  to   100 
marriages '  ? 

4.  The  great  famine  in  Ireland  began  in  1845  an(^  reached 
its  climax  in  1848.     During  this  time  agrarian  crime  increased 
very  rapidly,  until,  in  1848,  it  was  more  than  three  times  as 
great  as  in  1 845 .     After  this  time  it  decreased  with  the  return 
of  better  crops,  until,  in  185 1,  it  was  only  50  per  cent  more  than 
it  was  in  1845.     I*  *s  evident  from  this  that  a  close  relation 
of  cause  and  effect  exists  between  famine  and  agrarian  crime. 
(Hyslop.) 

5.  Sachs  maintained,  in  1862,  that  starch  is  formed  by  the 
decomposition  in  chlorophyl  of  carbon- dioxide  gas  under  the 
influence  of  light.      He  found  that  when  all  other  conditions 
were  constant,  and  light  was  excluded  from  a  plant,  no  starch 
was  formed ;  the  single  circumstance  of  readmitting  light  was 
accompanied  by  renewed  formation  of  starch.      Further,  he 
found  that  if  certain  portions  of  the  leaves  of  an  illuminated 
plant  were  covered  with  black  paper,  no  starch  was  found  in 
these  portions. 

6.  Jupiter  gives  out  more  light  than  it  receives  from  the  sun. 
What  is  the  obvious  conclusion,  and  by  what  method  is  it 
reached  ? 

7.  What  methods  would  you  employ  in  order  to  test  the 
truth  of  the  proposition,  omne  vivum  ex  vivo  ? 


QUESTIONS  AND   EXERCISES  375 

8.  War  is  a  blessing,  not  an  evil.     Show  me  a  nation  that 
has  ever  become  great  without  blood-letting. 

9.  If  wages  depend  upon  the  ratio  between  the  amount  of 
labor-seeking  employment,  and  the  amount  of  capital  devoted 
to  its  employment,  the  relative  scarcity  or  abundance  of  one 
factor  must  mean  the  relative  abundance  or  scarcity  of  the 
other.     Thus  capital  must  be  relatively  abundant  where  wages 
are  high,  and  relatively  scarce  where  wages  are  low.      Now,  as 
the  capital  used  in  paying  wages  must  largely  consist  of  the 
capital-seeking  investment,  the  current  rate  of  interest  must  be 
the  measure  of  its  relative  abundance  or  scarcity.     So  if  it  be 
true  that  wages  depend  upon  the  ratio  between  the  amount  of 
labor-seeking  employment,  and  the  capital  devoted  to  its  em- 
ployment, then  high  wages  must  be  accompanied  by  low  inter- 
est, and,  reversely,  low  wages  must  be  accompanied  by  high 
interest.     This  is  not  the  fact  but  the  contrary.     (George.) 

10.  Construct  an  inductive  argument  to  prove  that  some 
article  of  food,  or  some  habit,  is  beneficial  or  injurious  to  you, 
and  analyze  your  reasoning,  showing  the  methods  which  you 
have  employed. 

11.  Some  comets  have  been  observed  to  have  the  same 
orbits  as  certain  meteoric  showers.     The  hypothesis  is  suggested 
that  all  meteoric  showers  may  represent  the  de"bris  of  disinte- 
grated comets.       Biela's  comet  having  been  missing  for  some 
time,  it  was  accordingly  predicted  that  when  next  due  it  would 
be  replaced  by  a  meteoric  shower.     This  prediction  was  verified 
by  observation. 

12.  Tyndall  found  that  of  twenty-seven  sterilized  flasks  con- 
taining infusion  of  organic  matter,  and  opened  in  pure  Alpine 
air,  not  one  showed  putrefaction ;  while  of  twenty-three  similar 
flasks,  opened  in  a  hay-loft,  only  two  remained  free  from  putre- 
faction after  three  days.      He  concluded  that  putrefaction  is 
due  to  floating  particles  in  the  air. 


376  QUESTIONS  AND   EXERCISES 

13.  'Whether   or   not   a  bad  theory  is  better  than  none^ 
depends  upon  circumstances.'      Examine  this  statement,  and 
point  out  what  are  some  of  the  circumstances  of  which  mention 
is  made. 

14.  It  is  said  that  a  general  resemblance  of  the  hills  near 
Ballarat  in  Australia  to  the  Californian  hills  where  gold  had 
been  found  suggested  the  idea  of  digging  for  gold  at  Ballarat. 
(Minto.) 

15.  There  are  no  great  nations  of  antiquity  but  have  fallen 
to  the  hand  of  time  ;  and  England  must  join  them  to  complete 
the  analogy  of  the  ages.     Like  them  she  has  grown  from  a 
birth-time  of  weakness  and  tutelage  to  a  day  of  manhood  and 
supremacy  ;    but  she  has  to  face  her  setting.      Everything  that 
grows  must  also  decay.     (Edinburgh,  1893.) 

1 6.  Goldscheider  proved  that  muscular  sensations  play  no 
considerable  part  in  our  consciousness  of  the  movements  of  our 
limbs,  by  having  his  arm  suspended  in  a  frame  and  moved  by 
an  attendant.      Under   these   circumstances,  where  no  work 
devolved  on  his  muscles,  he  found  that  he  could  distinguish  as 
small  an  angular  movement  of  the  arm  as  when  he  moved  and 
supported  it  himself. 

"  17.  Goldscheider  also  proved  that  the  chief  source  of  move- 
ment-consciousness is  pressure  sensations  from  the  inner  sur- 
face of  the  joints,  by  having  his  arm  held  so  that  the  joint 
surfaces  were  pressed  more  closely  together,  and  finding  that 
a  smaller  movement  was  now  perceptible. 

1 8.  Wages  in  the  United  States  are  higher  than  in  England, 
because  the  former  country  is  a  republic  and  has  a  protective 
tariff. 

19.  It  does  not  follow  that  an  institution  is  good  because  a 
country  has  prospered  under  it,  nor  bad  because  a  country  in 
which  it  exists  is  not  prosperous.     It  does  not  even  follow  that 
institutions  to  be  found  in  all  prosperous  countries,  and  not 


QUESTIONS   AND   EXERCISES  377 

to  be  found  in  backward  countries,  are  therefore  beneficial. 
For  this  at  various  times  might  confidently  have  been  asserted 
of  slavery,  of  polygamy,  of  aristocracy,  of  established  churches  ; 
and  it  may  still  be  asserted  of  public  debts,  of  private  property 
in  land,  of  pauperism,  and  of  the  existence  of  distinctly  vicious 
or  criminal  classes.  (George.) 

20.  Explain  the  procedure  of  the  reductio  ad  absurdum  form 
of  argument. 

21.  It  may  be  a  coincidence   merely;  but,  if  so,  it  is  re- 
markably strange  that  while  the  chloroform  has  not  changed, 
while  the  constitutions  of  the  patients  have  not  changed,  where 
the  use  of  the  inhaler  is  the  rule  there  are  frequent  deaths  from 
chloroform ;  whilst  in  Scotland  and  Ireland,  where  the  use  of 
the  inhaler  is  the  exception,  deaths  are  proportionally  rare. 

22.  We  should  think  it  a  sin  and  shame  if  a  great  steamer, 
dashing  across  the  ocean,  were  not  brought  to  a  stop  at  a  signal 
of  distress  from  the  mere  smack.  .  .  .     And  yet  a  miner  is 
entombed  alive,  a  painter  falls  from  a  scaffold,  a  brakeman  is 
crushed  in  coupling  cars,  a  merchant  fails,  falls  ill  and  dies,  and 
organized  society  leaves  widow  and   child  to  bitter  want  or 
degrading  alms.     (George,  Protection  and  Free  Traded) 

23.  Manufacturing    countries    are    always    rich    countries ; 
countries  that  produce  raw  material  are  always  poor.     There- 
fore, if  we  would  be  rich,  we  must  have  manufactures,  and  in 
order  to  get  them,  we  must  encourage  them.  .  .  .     But  I  could 
make  as  good  an  argument  to  the  little  town  of  Jamaica  .  .  . 
in  support  of  a  subsidy  to  a  theatre,  I  could  say  to  them :  all 
cities  have  theatres,  and  the  more  theatres  it  has  the  larger  the 
city.     Look  at  New  York  !  .  .  .     Philadelphia  ranks  next  to 
New  York  in  the  number  and  size  of  its  theatres,  and  therefore 
comes  next  to  New  York  in  wealth  and  population.  ...     I 
might  then  drop  into  statistics  .  .  .  and  point  to  the  fact  that 
when  theatrical  representations  began  in  this  country,  its  popu- 


3/8  QUESTIONS  AND   EXERCISES 

lation  did  not  amount  to  a  million,  that  it  was  totally  destitute 
of  railroads,  and  without  a  single  mile  of  telegraph  wire.  Such 
has  been  our  progress  since  theatres  were  introduced  that  the 
census  of  1880  showed  we  had  50,155,783  people,  90,907  miles 
of  railroad,  and  291,212-^  miles  of  telegraph  wires.  (George, 
Protection  and  Free  Trade.) 

24.  What  methods  would  you  employ  to  investigate  the  con- 
nection between  changes  in  the  barometer  and  in  the  weather  ? 

25.  In  Sir  Humphry  Davy's  experiments  upon  the  decom- 
position  of  water   by  galvanism,  it  was   found   that,  besides 
the  two  components  of  water,  oxygen  and  hydrogen,  an  acid 
and  an  alkali  were  developed  at  the  two  opposite  poles  of  the 
machine.     The  insight  of  Davy  conjectured  that  there  might 
be  some  hidden  cause  of  this  portion  of  the  effect :  the  glass 
containing   the  water   might   suffer   partial  decomposition,  or 
some  foreign  matter  might  be  mingled  with  the  water,  and  the 
acid  and  alkali  be  disengaged  from  it,  so  that  the  water  would 
have  no  share  in  their  production.  ...     By  the  substitution  of 
gold  vessels  for  glass,  without  any  change  in  the  effect,  he  at 
once  determined  that  the  glass  was  not  the  cause.     Employing 
distilled  water,  he  found  a  marked  diminution  of  the  quantity 
of  acid  and  alkali  evolved ;  yet  there  was  enough  to  show  that 
the  cause,  whatever  it  was,  was  still  in  operation.  .  .  .     He 
now  conceived  that  the  perspiration  from  the  hands  touching 
the  instruments   might  affect   the   case,  as    it  would    contain 
common  salt,  and  an  acid  and  an  alkali  would  result  from  its 
decomposition  under  the  agency  of  electricity.     By  carefully 
avoiding  such  contact,  he  reduced  the  quantity  of  the  products 
still  further  until  no  more  than  slight  traces  of  them  were  per- 
ceptible.    An  experiment  determined  this :    the  machine  was 
put  under  an  exhausted  receiver,  and  when  thus  secured  from 
atmospheric  influence,  it  no  longer  evolved  the  acid  and  the 
alkali.     (Gore,  The  Art  of  Scientific  Discovery?) 


QUESTIONS  AND   EXERCISES  379 

26.  Properties  known  to  exist  in  potassium  have  been  pre- 
dicted of  and  found  to  exist  in  rubidium;    for  instance,  the 
carbonates  of  sodium  and  potassium  are  not  decomposed  by 
a  red  heat,  neither  are  those  of  rubidium,  or  caesium.     Some 
of  the  statements  which  are  true  of  chlorine  have  been  found  to 
be  true,  in  varying  degrees,  of  bromine  and  iodine.  .  .  .     After 
I  had  found  the  molecular  change  in  antimony  electro-deposited 
from  its  chloride,  I  sought  for  and  discovered  it  in  that  de- 
posited from  its  bromide  and  iodide ;  and  after  having  found 
magnetic  changes  in  iron  by  heat,  I  also  found  similar  ones  in 
nickel.     (Gore,  The  Art  of  Scientific  Discovery^) 

27.  What   inductive   fallacy   may   David   be   said   to  .have 
committed  when  he  said  in  his  haste  that  all  men  are  liars  ? 

28.  It  has  been  found  that  linnets  when  shut  up  and  edu- 
cated with  singing  larks  —  the  skylark,  woodlark,  or  titlark — • 
will  adhere  entirely  to  the  songs  of  these  larks,  instead  of  the 
natural   song   of  the   linnets.     We    may  infer,  therefore,  that 
birds  learn  to  sing  by  imitation,  and  that  their  songs  are  no 
more  innate  than  language  is  in  man.     (Hyslop.) 

29.  We  observe  very  frequently  that  very  poor  handwriting 
characterizes  the  manuscripts  of  able  men,  while  the  best  hand- 
writing is  as  frequent  with  those  who  do  little  mental  work 
when  compared  with  those  whose  penmanship  is  poor.     We 
may,  therefore,  infer  that  poor  penmanship  is  caused  by  the 
influence  of  severe  mental  labor.     (Hyslop.) 

30.  Galileo  describes  his  invention  of  the  telescope  as  fol- 
lows :     This    then  was   my   reasoning ;     this   instrument    [of 
which  he  had  heard  a  rumor]  must  either  consist  of  one  glass, 
or  of  more  than  one ;  it  cannot  be  of  one  alone,  because  its 
figure  must  be  either  concave  or  convex,  or  comprised  within 
two  parallel  superficies,  but  neither  of  these  shapes  alter  in  the 
least  the  objects  seen,  although  increasing  or  diminishing  them  ; 
for  it  is  true  that  the  concave  glass  diminishes,  and  that  the 


380  QUESTIONS  AND   EXERCISES 

convex  glass  increases  them  ;  but  both  show  them  very  indis- 
tinctly, and  hence  one  glass  is  not  sufficient  to  produce  the 
effect.  Passing  on  to  two  glasses,  and  knowing  that  the  glass 
of  parallel  superficies  has  no  effect  at  all,  I  concluded  that  the 
desired  result  could  not  possibly  follow  by  adding  this  one  to 
the  other  two.  I  therefore  restricted  my  experiments  to  com- 
binations of  the  other  two  glasses  ;  and  I  saw  how  this  brought 
me  to  the  result  I  desired.  (Quoted  by  Gore,  The  Art  of  Scien- 
tific Discovery.) 

31.  Darwin  was  struck  by  the  number  of  insects  caught  by 
the  leaves  of  the  common  sun-dew.     It  soon  became  evident 
to  him  that  "  Drosera  was  excellently  adapted  for  the  special 
purpose  of  catching  insects."  ...     As  soon  as  he  began  to 
work  on  Drosera,  and  was  led  to  believe  that  the  leaves  ab- 
sorbed nutritious  matter  from  the  insects,  he  began  to  reason 
by  analogy  from  the  well-understood  digestive  capacity  of  ani- 
mals. .  .  .     Having  by  analogy  established  the  power  of  di- 
gestion in  plants,  analogy  led  him  to  seek  in  plants  the  elements 
that  do  the  work  of  digestion  in  animals.     Bringing  together 
what  was  known  of  plants,  he  pointed  out  that  the  juices  of 
many  plants  contain  an  acid,  and  so  one  element  of  a  digestive 
fluid  was  at  hand ;    and  that  all  plants  possess  the  power  of 
dissolving  albuminous  or  proteid  substances,  protoplasm,  chlo- 
rophyl,  etc.,  and  that  "  this  must  be  effected  by  a  solvent,  proba- 
bly consisting  of  ferment  together  with  an  acid."    After  writing 
the  last-quoted  sentence,  he  learned  that  a  ferment  which  con- 
verted  albuminous   substances   into  true  peptones  had  been 
extracted  from  the  seeds  of  the  vetch.     (Cramer,  The  Method 
of  Darwin.) 

32.  Strongly  impressed  with  the  belief  that  some  '  harmonic ' 
relation  must  exist  among  the  distances  of  the  several  planets 
from  the  sun,  and  also  among  the  times  of  their  revolution, 
Kepler  passed  a  large  part  of  his  early  life  in  working  out  a 


QUESTIONS  AND   EXERCISES  381 

series  of  guesses  at  this  relation,  some  of  which  now  strike  us 
as  not  merely  most  improbable,  but  positively  ridiculous.  His 
single-minded  devotion  to  truth,  however,  led  him  to  abandon 
each  of  these  hypotheses  in  turn  so  soon  as  he  perceived  its 
fallacy  by  submitting  it  to  the  test  of  its  conformity  to  observed 
facts.  .  .  .  But  he  was  at  last  rewarded  by  the  discovery  of 
that  relation  between  the  times  and  the  distances  of  the  planet- 
ary revolutions,  which  with  the  discovery  of  the  ellipticity  of  the 
orbits,  and  of  the  passage  of  the  radius  vector  over  equal  areas 
in  equal  times  has  given  him  immortality  as  an  astronomical 
discoverer.  But  ...  he  was  so  far  from  divining  the  true 
rationale  of  the  planetary  revolutions  that  he  was  led  to  the 
discovery  of  the  elliptical  orbit  of  Mars  by  a  series  of  happy 
accidents  .  .  .  whilst  his  discovery  of  the  true  relations  of 
times  and  distances  was  the  fortunate  guess  which  closed  a 
long  series  of  ^fortunate  ones,  many  of  which  were  no  less 
ingenious. 

Now  it  was  by  a  grand  effort  of  Newton's  constructive  imagi- 
nation, based  on  his  wonderful  mastery  of  geometrical  reason- 
ing, that,  starting  with  the  conception  of  two  forces,  one  of 
them  tending  to  produce  continuous  uniform  motion  in  a 
straight  line,  the  other  tending  to  produce  a  uniformly  acceler- 
ated motion  towards  a  fixed  point,  he  was  able  to  show  that  if 
these  dynamical  assumptions  were  granted,  Kepler's  laws,  being 
consequences  of  them,  must  be  universally  true.  And  it  was 
his  still  greater  glory  to  divine  the  profound  truth  that  the  fall 
of  the  moon  towards  the  earth  —  that  is  the  deflection  of  her 
path  from  a  tangential  line  to  an  ellipse  —  is  a  phenomenon  of 
the  same  order  as  the  fall  of  a  stone  to  the  ground.  (Gore,  The 
Art  of  Scientific  Discovery.) 

33.  After  Franklin  had  investigated  the  nature  of  electricity 
for  some  time,  he  began  to  consider  how  many  of  the  effects 
of  thunder  and  lightning  were  the  same  as  those  produced  by 


382  QUESTIONS  AND   EXERCISES 

electricity.  Lightning  travels  in  a  zig-zag  line,  and  so  does  an 
electric  spark ;  electricity  sets  things  on  fire,  so  does  lightning ; 
electricity  melts  metals,  so  does  lightning.  Animals  can  be 
killed  by  both,  and  both  cause  blindness.  Pointed  bodies 
attract  the  electric  spark,  and  in  the  same  way  lightning  strikes 
spires,  and  trees,  and  mountain  tops.  Is  it  not  likely  then  that 
lightning  is  nothing  more  than  electricity  passing  from  one 
cloud  to  another,  just  as  an  electric  spark  passes  from  one  sub- 
stance to  another  ?  (Buckley,  A  Short  History  of  Natural 
Science.) 

34.  How   did   Franklin   proceed  to  verify  the  hypothesis 
stated  in  the  last  example  ? 

35.  Galileo  discovered  by  means  of  his  telescope  that  Jupi- 
ter has  four  moons,   instead  of  one  like  the  earth,  and  he 
regarded  this  discovery  as  a  confirmation  of  the  Copernican 
theory.      Explain   the   nature   of  the   reasoning   involved   in 
reaching  this  conclusion. 

36.  That  the  period  of  tide  should  be  accidentally  the  same 
as  that  of  the  culmination  of  the  moon,  that  the  period  of  the 
highest  tide  should  be  accidentally  the  same  as  the  syzygies,  is 
possible  in  abstracto  ;  but  it  is  in  the  highest  degree  improb- 
able :  the  far  more  probable  assumption  is,  either  that  the  sun 
and  moon  produce  the  tide,  or  that  their  motion  is  due  to  the 
same  grounds  as  the  motion  of  the  tide.     (Hibben.) 

37.  During  the  retreat  of  the  Ten  Thousand  a  cutting  north 
wind  blew  in  the  faces  of  the  soldiers,  sacrifices  were  offered 
to  Boreas,  and  the  severity  of  the  wind  immediately  ceased, 
which  seemed  a  proof  of  the  god's  causation.     (Hibben.) 

38.  A  nectary  implies  nectar,  but  Sprengel  had  come  to  the 
conclusion  that  orchis  morio  and  orchis  maculata,  though  fur- 
nished with  nectaries,  did  not  secrete  nectar.     Darwin  examined 
the  flowers  of  orchis  morio  for  twenty-three  consecutive  days, 
looking  at  them  after  hot  sunshine,  after  rain,  and  at  all  hours ; 


QUESTIONS  AND   EXERCISES  383 

he  kept  the  spikes  in  water  and  examined  them  at  midnight 
and  early  the  next  morning.  He  irritated  the  nectaries  with 
bristles,  and  exposed  them  to  irritating  vapors.  He  examined 
flowers  whose  pollinia  had  been  removed,  and  others  which 
would  probably  have  them  soon  removed.  But  the  nectary 
was  invariably  dry. 

He  was  thoroughly  convinced,,  however,  that  these  orchids 
require  the  visits  of  insects  for  fertilization,  and  that  insects 
visit  flowers  for  the  attractions  offered  in  the  way  of  nectar,  and 
yet  that  in  these  orchids  the  ordinary  attraction  was  absent. 
In  examining  the  orchids  he  was  surprised  at  the  degree  to 
which  the  inner  and  outer  membranes  forming  the  tube  or 
spur  were  separated  from  each  other,  also  at  the  delicate  nature 
of  the  inner  membrane,  and  the  quantity  of  fluid  contained 
between  the  two  membranes.  He  then  examined  other  forms 
that  do  secrete  nectar  in  the  ordinary  way,  and  found  the  mem- 
branes closely  united,  instead  of  separated  by  a  space.  "  I  was 
therefore  led  to  conclude,"  he  says,  "  that  insects  penetrate  the 
lax  membrane  of  the  nectaries  of  the  above-named  orchids  and 
suck  the  copious  fluid  between  the  two  membranes."  He 
afterwards  learned  that  at  the  Cape  of  Good  Hope  moths  and 
butterflies  penetrate  peaches  and  plums,  and  in  Queensland  a 
moth  penetrates  the  rind  of  the  orange.  These  facts  merely 
proved  his  anticipation  less  anomalous  than  it  had  seemed. 
(Cramer,  The  Method  of  Darwin?) 

39.  Construct  an  hypothesis  to  explain  some  fact  of  your 
experience,  and  explain  how  it  may  be  either  verified  or  over- 
thrown. 

40.  When  Darwin  began  to  work  on  Drosera  he  was  led 
to  believe  that  the   leaves   absorbed   nutritious   matter   from 
insects.     He  then  reasoned  by  analogy  from  the  well -under- 
stood digestive   capacity  of  animals.     He   made  preliminary 
'crucial'  experiments  by  immersing  some  leaves  of  Drosera 


384  QUESTIONS  AND    EXERCISES 

in  nitrogeneous  and  others  in  non-nitrogeneous  fluids  of  the 
same  density  to  determine  whether  the  former  affected  the 
leaves  differently  from  the  latter.  This  he  found  to  be  the  case. 
He  then  experimented  with  solid  animal  matter  and  found 
that  the  leaves  are  capable  of  true  digestion.  Analogy  then 
led  him  to  seek  in  plants  the  elements  that  do  the  work  of 
digestion  in  animals.  He  pointed  out  that  the  juices  of  many 
plants  contain  an  acid,  and  so  one  element  of  a  digestive  fluid 
was  at  hand  ;  and  that  all  plants  possess  the  power  of  dissolving 
albuminous  or  proteid  substance-protoplasm,  chlorophyl,  and 
that  this  must  be  effected  by  a  solvent  consisting  probably 
of  a  ferment  together  with  an  acid.  Afterwards  he  learned 
that  a  ferment  which  converted  albuminous  substances  into 
true  peptones  had  been  extracted  from  the  seeds  of  the  vetch. 
(Cramer,  The  Method  of  Darwin,  pp.  95-99.) 

41.  In  opposition  to  the  facts  stated  above,  Tischutkin 
maintains  that  the  '  digestion '  of  insectivorous  plants  is  not 
accomplished  in  the  same  way  as  in  animals,  but  is  due  to 
bacteria  :  that  the  pepsin  is  not  a  secretion  of  the  plant,  but 
a  by-product  of  the  activity  of  the  bacteria.  Suppose  that  this 
theory  is  true,  and  Darwin's  false,  what  would  you  say  regard- 
ing the  character  of  the  latter's  reasoning  ? 

PART   III. —THE  NATURE  OF  THOUGHT 
CHAPTER  XX.  — Judgment  the  Elementary  Process 

1.  What  objections  are  there  to  speaking  of  thought  as  'a 
thing  like  other  things  '  ? 

2.  What  is  the  general  law  of  Evolution?    .Explain  what  is 
meant  by  a  change  from  the  homogeneous  to  the  heterogene- 
ous. 

3.  What  general  conclusions  are  reached  by  the  application 
of  the  law  of  Evolution  to  the  thought-process  ? 


QUESTIONS  AND   EXERCISES  385 

4.  What  do  you  understand  by  Judgment?     How  does  a 
simple  judgment  differ  from  sensation? 

5.  In  what  sense  may  our  judgments  be  said  to  be  the  union 
of  two  concepts  ? 

6.  Would  the  doctrine  that  in  knowing  we  first  have  Simple 
Apprehension,  then  as  separate  intellectual  processes,  Judgment 
and  finally  Inference,  agree  with  the  general  evolutionary  view 
of  consciousness  ?     Explain  fully. 

CHAPTER  XXI. —  The  Characteristics  of  Judgment 

1.  What  do  you  understand  by   the  universality  of  judg- 
ments ?     What  is  the  distinction  between  the  universality  of  a 
judgment  and  that  of  a  proposition? 

2.  How  would  you  prove  that  all  judgments  are  universal? 

3.  Is  any  judgment  necessary  in  itself?     If  not,  whence  do 
judgments  derive  their  necessity? 

4.  What  is  the  argument  by  which  it  has  been  maintained 
that  there  must  be  judgments  or  principles  which  are  in  them- 
selves necessary? 

5.  Explain  how  it  is  possible  for  a  judgment  to  be  at  once 
both  analytic  and  synthetic. 

6.  Explain  what  is  meant  by  a  ( system  '  of  knowledge. 

7.  When  judgment  brings  new  facts  into  relation  to  what 
we  already  know,  does  the  old  body  of  knowledge  undergo  any 
modification  ? 

CHAPTER  XXII.  —  The  Laws  of  Thought 

1.  In  what  sense  can  we  speak  of  a  law  of  Thought? 

2.  Explain  what  is  meant  by  the  law  of  Identity. 

3.  How  has  this  law  been  interpreted  by  Boole  and  Jevons? 

4.  What  does  Jevons  mean  by  the  '  substitution  of  similars,' 
and  how  does  he  propose  to  employ  this  principle  ? 

2C 


386  QUESTIONS  AND   EXERCISES 

5.  What   objections   are   there    to    employing   the   sign  of 
equality   to   represent   the  relation  between  the  subject  and 
predicate  of  a  judgment? 

6.  Explain  how  the  law  of  Identity  is  related  to  the  charac- 
teristics of  judgment  treated  in  the  last  chapter. 

7.  What  is  the  meaning  of  the  law  of  Contradiction? 

8.  Explain  the  use  of  the  law  of  Excluded  Middle. 

CHAPTER  XXIII.  —  Types  of  Judgment 

1.  Why  do  we  begin  with  judgments  of  Quality? 

2.  Explain  how  we  pass  in  the  development  of  intelligence 
from  Quality  to  Quantity. 

3.  In  what  sense  is  it  true  that  judgments  of  Quantity  never 
give  us  the  real  nature  of  things,  but  only  their  relation  to 
something  else? 

4.  What  is  meant  by  anthropomorphic  causes?     How  are 
they  distinguished  from  scientific  causes? 

5.  What  new  element  did  the  discovery  of  the  law  of  the 
Conservation  of  Energy  introduce  in  the  causal  conception  as 
employed  in  certain  sciences? 

6.  Why  cannot  this  new  extension  have  any  application  in 
the  field  of  the  mental  sciences? 

7.  How  does  the  standpoint  of  judgments  of  Individuality 
differ  from  that  of  judgments  of  Causality? 

CHAPTER  XXIV.  —  Inference 

1.  How  does  Inference  differ  from   Judgment?     In  what 
sense  may  it  be  said  that  it  is  an  extension  of  the  latter  pro- 
cess? 

2.  Does  the  passage  from  Judgment  to  Inference  illustrate 
the  general  law  of  Logical  Evolution?     Explain. 


QUESTIONS   AND   EXERCISES  387 

3.  In   the   development  of  our  knowledge,   which  usual)) 
comes  first,  premises  or  conclusion? 

4.  How  is  it  possible  to  pass  from  the  known  to  the  un- 
known ? 

5.  Explain  under  what  circumstances  only  an  Inference  is 
possible. 

6.  What  is  the  common  element   in  both  Induction  and 
Deduction?     How  do  they  differ? 

CHAPTER  XXV.  —  Rational  and  Empirical  Theories 

1.  Who  are  the  great  historical  representatives  respectively 
of  Rationalism  and  Empiricism? 

2.  Explain  the  method  and  procedure  of  Rationalism. 

3.  What  is  the  great  instrument  of  knowledge  according  to 
Rationalism?     What  according  to  Empiricism? 

4.  State  as  clearly  as  you  can  the  various  points  at  issue 
between  the  two  schools. 

5.  Explain  Mill's  theory  that  we  always  reason  from  one 
particular  fact  to  another.     How  far  do  you  agree  with  his 
conclusions? 

6.  Is  it  true  that  we  obtain  a  general  law  by  summing  up 
particulars  ? 

7.  Is  there  any  direct  and  necessary  connection  between  the 
number  of  instances  and  the  induction  of  the  general  law? 

8.  Criticise  Jevon's  theory  of  'Perfect  Induction'  as  stated 
on  page  187. 


INDEX 


Abstract,  two  Meanings  of  the  Word, 

Si- 
Accent,  the  Fallacies  of,  156. 

Accident,  the  Fallacy  of,  163. 

Agreement,  the  Method  of,  200;  De- 
ficiencies in  the  Method  of,  204. 

Amphiboly,  the  Fallacy  of,  156. 

Analogy,  Explanation  by  Means  of, 
219;  the  Principle  of,  221;  State- 
ment of  Law,  222;  its  Function  in 
suggesting  Hypothesis,  223 ;  its  Use 
by  Darwin,  225 ;  its  Incompleteness 
as  a  Method  of  Explanation,  226. 

Analysis,  its  Relation  to  Synthesis,  279. 

Anthropomorphism,  309. 

Apprehension,  Simple,  44. 

A  priori  Truths,  278. 

Argumentum,  ad  rem,  168 ;  ad  homi- 
nem,  168  ;  ad populum,  169  ;  ad  igno- 
rantiam,  169 ;  ad  verecundiam,  170. 

Aristotle,  Logic  of,  22 ;  List  of  Logical 
Works,  22 ;  his  Theory  of  the  Syllo- 
gism, 23;  Importance  of  Induction 
and  Deduction  in  his  Logic,  25  ;  his 
Classification  of  Fallacies,  152;  his 
Statement  of  the  Law  of  Contradic- 
tion, 295. 

Art,  an,  its  Relation  to  a  Science,  8. 

B 
Bacon,  Logic  of,  28  ;   his  Method,  28  ; 

on  the  Tendency  to  neglect  Negative 

Instances,  257 ;  his  Idols  of  the  Cave, 

257. 
Bosanquet,  his  Views  of  Logic,  n.note ; 

his  Writings  on  Modern  Logic,  17 ; 

his  Remarks  on  Analogy,  227. 
Bradley,  12. 


Cant  Words  and  Phrases,  249. 
Causal  Connection,  Judgments  of,  307. 


Cause,  the  Fallacy  of  the  False,  171 ; 
the  Development  of  the  Principle  of, 
3°9- 

Causes,  the  Plurality  of,  204. 

Chances,  the  Calculation  of,  194. 

Circle,  Argument  in  a,  165. 

Classification,  Principles  of,  74 ;  Rules 
of,  76;  of  Fallacies,  152,  246;  Aris- 
totle's, of  Fallacies,  152. 

Composition,  the  Fallacy  of,  160. 

Concepts  and  Judgments,  268. 

Conclusion,  the  Irrelevant,  168. 

Concrete,  two  Senses  of  the  Word, 

51- 

Consequent,  Fallacy  of  the,  170. 
Conservation  of  Energy,  the  Law  of, 

and  its  Influence  on  the  Conception 

of  Cause,  313. 

Contradiction,  the  Law  of,  38,  295. 
Conversion,  the,  of  Propositions,  100 ; 

Simple,   101 ;     by   Limitation,   101 ; 

by  Contraposition,  102;    Errors   in, 


Darwin,  his  Power  of  arresting  Ex- 
ceptions, 217  ;  his  Use  of  Analogy, 
225 ;  his  Employment  of  Hypotheses, 
232. 

Deduction,  its  Relation  to  Induction, 
329- 

Definition,  the  Necessity  of,  63 ;  Verbal 
and  Real,  63 ;  Ways  of  Regarding) 
64 ;  Socrates'  Search  for,  65 ;  Rules 
of,  69. 

Descartes,  29,  335. 

Dialectic,  Socrates'  Use  of,  65. 

Dichotomy,  72. 

Difference,  Method  of,  205. 

Differentia,  68. 

Dilemma,  the  simple  Constructive,  149  ; 
the  Complex  Constructive,  150;  the 
Complex  Destructive,  150. 


389 


390 


INDEX 


Division,  Rules  for,  76 ;  the  Fallacy  of, 
162. 

E 

Empiricism,  the  Doctrine  of,  337. 

Enthymemes,  41,  126. 

Enumeration,  as  the  Starting-point  of 
Induction,  185;  Judgments  of,  305. 

Episyllogisms  and  Prosyllogisms,  127. 

Equivocation,  the  Fallacies  of,  159. 

Ethics,  its  Standpoint  compared  with 
that  of  Psychology,  316. 

Euler,  no. 

Evolution,  the  Law  of,  262;  the  Appli- 
cation of  the  Law  of,  to  Thought,  264. 

Excluded   Middle,  the  Law  of,  72,  297. 

Experiment  and  Observation,  180; 
Advantages  of  employing,  180. 

Explanation  and  Observation,  177 ;  the 
Problem  of,  182. 

Extension  and  Intension  of  Terms,  55. 


Fallacies,  Classification  of,  152,  246; 
Syllogistic,  149  ;  Inductive,  245  ;  the 
Source  of,  245 ;  of  Interpretation, 
154 ;  occasioned  by  Language,  246 ; 
of  Reasoning,  157,  254 ;  of  Observa- 
tion, 250 ;  Individual,  257. 

Figures  of  the  Syllogism,  113;  the 
Special  Canons  of  the  four,  117 ;  De- 
termination of  the  Valid  Moods  in, 
120;  the  Perfect,  123 ;  the  Imperfect, 
123 ;  Reduction  of,  123 ;  the  Organic 
Relation  of,  125,  note. 


Galen,  123. 

Generalization,  Danger  of  hasty,  256. 
Genus,  its  Definition,  68. 
Guericke,  239. 

H 

Hegel,  Quotation  from  his  Logic,  n; 
his  Influence  on  the  Development  of 
Logic,  31. 

Herschel,  J.,  30. 

Hypothesis,  Reasoning  from  an,  230; 
the  Employment  of,  to  explain  Com- 
mon Events,  231 ;  Darwin's  Use  of, 


232;  the  Necessity  for  an,  233; 
Formation  of,  234;  the  Function  of 
Analogy  in  suggesting,  223,  236;  the 
Proof  of,  237;  Requirements  of  a 
Good,  240. 

I 

Identity,  the  Law  of,  38,  288;  Je- 
vons's  Interpretation  of  the  Law  of, 
289. 

Ignoratio  Elenchi,  166. 

Imagination,  its  Part  in  the  Formation 
of  Theories,  234. 

Individuality,  Judgments  of,  315. 

Induction  and  Deduction,  2,  24,  329; 
the  Baconian  Method  of,  28 ;  Mill's 
Emphasis  on,  31;  the  Problem  of, 
172;  Perfect  and  Imperfect,  187. 

Inference,  Mediate  and  Immediate,  92; 
the  Nature  of,  324 ;  as  distinguished 
from  Judgment,  318 ;  the  Paradox 
of,  325  ;  as  a  Development  of  Judg- 
ment, 328  ;  and  Number  of  Instances, 
344.  (See  also  Reasoning.) 

Instances,  the  Value  of  Numerous,  345. 

Intension  and  Extension  of  Terms,  55. 

Interpretation,  of  Propositions,  92; 
Errors  of,  154 ;  Judgment  a  Process 
of,  266. 

J 

James,  7. 

Jevons,  his  Account  of  Perfect  Induc- 
tion 187  ;  his  Calculation  of  Chances, 
195 ;  his  Interpretation  of  the  Law 
of  Identity,  289 ;  his  Principle  of  the 
Substitution  of  Similars,  289. 

Judgment,  the  Starting-point  of  Know- 
ledge, 266;  as  a  Process  of  Inter- 
pretation, 267;  and  Concept,  268; 
the  Universality  of,  274 ;  the  Neces- 
sity of,  276;  a  priori,  279;  as  involv- 
ing both  Analysis  and  Synthesis, 
279;  as  constructing  a  System  of 
Knowledge,  284;  its  Relation  to  In- 
ference, 318. 

Judgments,  of  Quality,  300;  of  Quan- 
tity, 304 ;  of  Enumeration,  305  ;  of 
Measure,  305 ;  of  Causal  Connec- 
tion, 307 ;  of  Individuality,  315. 


INDEX 


391 


Ladd,  7. 

Language,  Dangers  from  the  Careless 
Use  of,  6 1 ;  Fallacies  of,  246 ;  Figura- 
tive, 249. 

Law,  of  Identity,  38,  288 ;  of  Contra- 
diction, 38,  295 ;  of  Excluded  Mid- 
dle, 72,  297 ;  of  Conservation  of 
Energy,  313. 

Laws  of  Thought,  38,  72,  288. 

Locke,  as  the  Representative  of  Em- 
piricism, 30,  335 ;  on  the  Careless 
Use  of  Words,  61,  247. 

Logic,  Definition  of,  i ;  Derivation  of 
the  Word,  3 ;  Relation  to  Psychol- 
ogy, 4 ;  Comparison  with  Physiology, 
6 ;  as  a  Science  and  an  Art,  8 ;  Util- 
ity of,  10;  Necessity  of,  12;  the 
Materials  of,  13  ;  of  the  Sophists,  18  ; 
of  Socrates,  19;  of  Aristotle,  22,  32; 
of  the  Schoolmen,  26;  of  Bacon,  28  ; 
Development  of  Modern,  31 ;  the 
Equational,  289. 

Lyell,  his  Overthrow  of  the  'Catas- 
trophic '  Theory  in  Geology,  243. 


M 

Malthus,  his  Theories  of  Population, 
168,  225. 

Measure,  Judgments  of,  305. 

Mental  Operations,  proposed  Division 
of,  43- 

Metaphors,  Dangers  from  the  Use  of, 
250. 

Method,  the  Progressive  or  Synthetic, 
128 ;  the  Regressive  or  Analytic,  128 ; 
the,  of  Agreement,  200;  the,  of  Dif- 
ference, 205  ;  the  Joint,  of  Agreement 
and  Difference,  209;  the,  of  Con- 
comitant Variations,  211 ;  the,  of 
Residues,  213. 

Middle  Term,  the  Function  of  the,  106; 
Ambiguous,  160. 

Mill,  his  Importance  in  the  History  of 
Logic,  30;  his  Experimental  Meth- 
ods, 198  ;  his  View  of  the  Nature  of 
General  Principles,  339;  his  Doc- 
trine that  all  Reasoning  is  from  one 
Particular  Case  to  anotherr34o. 


Morphology,  compared  with  Psychol- 
ogy, 8. 

N 

Negative  Instances,  Tendency  to  neg- 
lect, 251. 

Neptune,  the  Discovery  of,  217. 

Newton,  his  Care  in  testing  Theories, 
239- 

Non  sequitur,  170. 

O 

Observation,    and    Explanation,    177 ; 

and    Experiment,    180;     Errors   of, 

250. 
Obversion,  the,   of   Propositions,   98 ; 

Errors  in,  155. 
Opposition,  the,  of  Propositions,  94. 


Perception,  as  involving  Judgment, 
266 ;  Difficulty  in  distinguishing  be- 
tween Inference  and,  253. 

Petitio  Principii,  165. 

Physiology  compared  with  Logic,  6. 

Plato,  in  the  History  of  Logic,  22 ;  and 
the  Doctrine  of  Reminiscence,  325. 

Post  hoc  propter  hoc,  171,  255. 

Predicables,  the,  67. 

Prejudices,  Individual,  257  ;  of  an  Age, 
258. 

Premises,  Definition  of,  40. 

Presumption,  Fallacies  of,  164. 

Propositions,  Categorical,  79;  Condi- 
tional, 79 ;  the  Nature  of,  78 ;  Qual- 
ity and  Quantity  of,  80;  Difficul- 
ties in  classifying,  83 ;  Relation  of 
Subject  and  Predicate  in,  85;  the 
Opposition  of,  94 ;  the  Obversion  of, 
98 ;  the  Conversion  of,  100. 

Psychology,  its  Relation  to  Logic,  4; 
Comparison  with  Morphology,  6; 
Comparison  with  Ethics,  316. 


Quality,  of  Propositions,  80;  Judg- 
ments of,  300. 

Quantity,  of  Propositions,  80;  Judg- 
ments of,  304. 

Quaternio  Terminorum,  158. 


392 


INDEX 


Question,  the  Fallacy  of  the  Complex, 

166. 
Question-Begging  Epithet,  248. 


R 

Rationalism,  its  Point  of  View,  335; 
the  Nature  of  its  Problems,  336 ;  its 
Neglect  of  Perception,  337. 

Reasoning,  the  Nature  of  Syllogistic, 
105;  Mediate,  92,  107;  Immediate, 
93;  Mistakes  in,  254 ;  Inductive  and 
Deductive,  329 ;  from  Particulars  to 
Particulars,  340 ;  from  Particulars  to 
a  ^niversal,  344.  (See  also  Infer- 
ence.) 

Reduction  of  the  Imperfect  Figures, 
123. 

Residues,  the  Method  of,  213. 


Schonbein,  his  Discovery  of  Ozone, 
217. 

Science,  as  related  to  Art,  8. 

Sigwart,  on  the  Difference  between 
Ancient  and  Modern  Science,  190; 
on  the  Application  of  Statistics,  191. 

Similars,  the  Principle  of  the  Substitu- 
tion of,  289. 

Socrates,  his  Sense  of  Ignorance,  4;  his 
Place  in  the  History  of  Logic,  20; 
his  Search  for  Definitions,  65;  his 
Employment  of  Dialectic,  66. 

Sophists,  the  Logic  of,  19;  Socrates' 
Refutation  of,  20;  Plato's  Criticism 


of  their  Theory  of  Knowledge,  22; 
their  Scepticism,  275. 
Sorites,  Aristotelian,   131;    Goclenian, 

Species,  Definition,  68. 

Spinoza,  as  a  Rationalist,  336. 

Statistics,  189. 

Stout,  7. 

Subject,  Relation  of  Predicate  and,  85. 

Syllogism,  the  Aristotelian,  23,  32;  the 
Nature  of  the,  36;  the  Principle  of 
the,  38 ;  the  Parts  of  the,  39 ;  the 
Rules  of  the,  103  ;  the  Figures  of  the, 
113  ;  the  Hypothetical,  136  ;  Rules  for 
the  Hypothetical,  137 ;  Relation  of 
Categorical  and  Hypothetical,  139; 
the  Disjunctive,  145  ;  Fallacies  of  the 
Disjunctive,  148. 

Synthesis,  its  Relation  to  Analysis,  279. 

System,  Difference  between  a,  and  an 
Aggregate,  285. 


Thales,  310. 

Thought,  the  Laws  of,  38 ;   the  Nature 

of,  260. 
Torricelli,  238. 


Variations,     of    Statistics,     193 ;     the 
Method  of  Concomitant,  211. 

W 

Whewell,  15,  30. 

Words,  the  Abuse  of,  61,  246. 


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